# Slope Form of Tangent: Ellipse

## Trending Questions

**Q.**Tangents are drawn to the ellipse x29+y25=1 at the ends of both latus rectum. The area of the quadrilateral so formed is

- 27 sq. units
- 132 sq. units
- 154 sq. units
- 45 sq. units

**Q.**

Find the condition for the line $x\mathrm{cos}\mathrm{\xce\pm}+y\mathrm{sin}\mathrm{\xce\pm}=p$ to be a tangent to the ellipse $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$

**Q.**A ray of light through (2, 1) is reflected at a point P on the y−axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity 13 and the distance of the nearer focus from this directrix is 8√53, then the equation of the other directrix can be

- 2x−7y+29=0 or 2x−7y−7=0
- 11x+7y+8=0 or 11x+7y−15=0
- 2x−7y−39=0 or 2x−7y−7=0
- 11x−7y−8=0 or 11x+7y+15=0

**Q.**The point P(−2√6, √3) lies on the hyperbola x2a2−y2b2=1 having eccentricity √52. If the tangent and normal at P to the hyperbola intersect its conjugate axis at the points Q and R respectively, then QR is equal to

- 3√6
- 6
- 6√3
- 4√3

**Q.**The locus of the foot of perpendicular drawn from the centre of the ellipse x2+3y2=6 on any tangent to it is:

- (x2−y2)2=6x2+2y2
- (x2−y2)2=6x2−2y2
- (x2+y2)2=6x2+2y2
- (x2+y2)2=6x2−2y2

**Q.**The equations of the tangents to the ellipse 9x2+16y2=144 from the point (2, 3) are

- x=2, y=3

- y=3, x=5

- x=3, y=2

- x+y=5, y=3

**Q.**If 3x+4y=12√2 is a tangent to the ellipse x2a2+y29=1 for some a∈R, then the distance between the foci of the ellipse is :

- 2√5
- 2√7
- 2√2
- 4

**Q.**Number of real tangents, which can be drawn from the point (4, 3) to the ellipse x216+y29=1, is

**Q.**If the complex number z1, z2 the origin form an equilateral triangle then z21+z22 =

**Q.**Tangents are drawn from the point (4, 2) to the curve x2+9y2=9, then the tangent of acute angle between the tangents is

- √435
- 3√35√17
- √317
- √4310

**Q.**If two concentric ellipses be such that the foci of one be on the other and if √32 and 1√2 be their eccentricities. Then angle between their axes is

- cos−11√6
- cos−123√3
- cos−1√23
- cos−1√23

**Q.**The equations of tangents drawn from the point (2, 3) to the ellipse 9x2+16y2=144 are:

- y=3
- y=5
- y=−x+3
- y=−x+5

**Q.**Let F1(x1, 0) and F2(x2, 0), for x1<0 and x2>0, be the foci of the ellipse x29+y28=1. Suppose a parabola having vertex at the origin and focus at F2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant.

If the tangents to the ellipse at M and N meet at R and the normal to tha parabola at M meets the x−axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF1NF2 is

- 4:5
- 5:8
- 3:4
- 2:3

**Q.**B is an extremity of the minor axis of the ellipse whose foci are S and S′. If ∠SBS′ is a right angle, then eccentricity of the ellipse is

- 12
- 1√2
- 23
- 13

**Q.**If two tangents to the ellipse x2a2+y2b2=1(a>b) make angles α and β with the major axis such that tanα+tanβ=λ, then the locus of their point of intersection is

- x2+y2=a2
- x2+y2=b2
- x2−a2=2λxy
- λ(x2−a2)=2xy

**Q.**If line x+y=3 is a tangent to the ellipse with foci at (4, 3) and (6, k) at point (1, 2), then the value of k is

- 27
- 17
- 20
- 15

**Q.**If tangents PQ and PR are drawn from a point on the circle x2+y2=16 to the ellipse x2a2+y212=1 (a<3), so that the fourth vertex S of the parallelogram PQSR lies on the circumcircle of the triangle PQR, then the eccentricity of the ellipse is

- 23
- √23
- 1√3
- √23

**Q.**A straight line PQ touches the ellipse x216+y29=1 and the circle x2+y2=r2 (3<r<4). RS is chord of the circle which is parallel to PQ and passes through any focus of ellipse, then the length of RS is equal to

**Q.**Let E be the ellipse x29+y24=1 and C be the circle x2+y2=9. Let P and Q be the points (1, 2) and (2, 1) respectively. Then

- Q lies inside C but outside E
- Q lies outside both C and E
- P lies inside both C and E
- P lies inside C but outside E

**Q.**Tangents are drawn to the ellipse x216+y27=1 at the end points of the latus rectum. The area of quadrilateral formed by these tangents is

- 1283 sq. units
- 643 sq. units
- 2563 sq. units
- 323 sq. units

**Q.**The equation of the ellipse, whose axes are coincident with the co-ordinates axis and which touches the straight lines 3x−2y−20=0 and x+6y−20=0, is

- x240+y210=1
- x25+y28=1
- x210+y240=1
- x240+y230=1

**Q.**

The angle between tangents to the curves $y={x}^{2}$ and $x={y}^{2}$ at $\left(1,1\right)$ is :

$0$

${\mathrm{tan}}^{-1}1$

${\mathrm{tan}}^{-1}\left(\frac{3}{4}\right)$

${\mathrm{tan}}^{-1}\left(\frac{1}{3}\right)$

**Q.**

**Focus of hyperbola is **$(\xc2\pm 3,0)$** and equation of tangent is **$2x+y-4=0$**, find the equation of hyperbola is**

$4{x}^{2}\xe2\u20ac\u201c5{y}^{2}=20$

$5{x}^{2}\xe2\u20ac\u201c4{y}^{2}=20$

$4{x}^{2}\xe2\u20ac\u201c5{y}^{2}=1$

$5{x}^{2}\xe2\u20ac\u201c4{y}^{2}=1$

**Q.**The equations of the tangents to the hyperbola 3x2−4y2=12 which are parallel to the line 2x + y + 7 = 0 are

**Q.**Distance between the points on the curve 4x2+9y2=1, where tangent is parallel to the line 8x=9y, is 2√k, unit, then k=

**Q.**A series of concentric ellipses E1, E2, …, En are drawn such that En touches the extremities of the major axis of En−1 and the foci of En coincide with the extemities of minor axis of En−1. If the eccentricites of the ellipse are independent of n, then the value of the eccentricity, is

- √53
- √5−12
- √5−1√2
- 1√5

**Q.**Given ellipse x2+4y2=16 and parabola y2−4x−4=0.

The quadratic equation whose roots are the slopes of the common tangents to the parabola and the ellipse, is

- 5x2−1=0
- 3x2−1=0
- 2x2−1=0
- 15x2+2x−1=0

**Q.**Consider the parabola whose focus is at (0, 0) and tangent at vertex is x−y+1=0. Then

- the length of latus rectum is 2√2
- the length of the chord of parabola on the x-axis is 4√2
- equation of directrix is x−y−2=0
- tangents drawn to the parabola at the extremities of the chord 3x+2y=0 intersect at an angle of π3

**Q.**Tangents are drawn to the ellipse x216+y27=1 at the end points of the latus rectum. The area of quadrilateral formed by these tangents is

- 1283 sq. units
- 323 sq. units
- 643 sq. units
- 2563 sq. units

**Q.**If line x+y=3 is a tangent to the ellipse with foci at (4, 3) and (6, k) at point (1, 2), then the value of k is

- 27
- 17
- 20
- 15