# Point Form of Normal: Ellipse

## Trending Questions

**Q.**On the ellipse x28+y24=1, let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x+2y=0. Let S and S′ be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS′, then the value of (5−e2)⋅A is

- 12
- 14
- 6
- 24

**Q.**The equation x22−r+y2r−5+1=0 represent an ellipse if

**Q.**The locus of mid-points of the line segments joining (−3, −5) and the points on the ellipse x24+y29=1 is

- 36x2+16y2+90x+56y+145=0
- 9x2+4y2+18x+8y+145=0
- 36x2+16y2+72x+32y+145=0
- 36x2+16y2+108x+80y+145=0

**Q.**

On the portion of the straight line, $\text{x+2y=4}$intercepted between the axes, a square is constructed on the side of the line away from the origin. Then the point of intersection of its diagonals has co-ordinates

$2,3$

$3,2$

$3,3$

$2,2$

**Q.**The equation of the normal to the ellipse x218+y28=1 at the point (3, 2) is

- 3x - 2y = 5
- 3x + 2y = 5
- 2x - 3y = 5
- 2x + 3y = 5

**Q.**

Find Minimize Z=3x+9y subject to

x+3y≤60 , x≤y and x, y≥0

**Q.**If the normal at an end point of a latus rectum of an ellipse x2a2+y2b2=1 (a>b) passes through one extremity of the minor axis. Then the eccentricity of the ellipse is equal to

- √5−12
- 1514
- 12
- √√5−12

**Q.**Show that the circle on the chord xcosα+ ysinα= p

Of the circle x^2+ y^2= a^2 as diameter is x^2+ y^2 -a^2-2p( xcosα+ ysinα- p)=0

**Q.**If normal at point (6, 2) to the ellipse passes through its nearest focus (5, 2), having centre at (4, 2), then its eccentricity is

- 13
- 1√2
- 1√3
- 12

**Q.**The polar of point (2t, t-4)w.r.t the circle, x*2+y*2-4x-6y+1=0 passes through the point

**Q.**The equation of normal at point P(8√2, 1) on the ellipse x2144+y29=1 is

- √2 x+y=15
- √2 x−y=15
- x+√2 y=15
- x−√2 y=15

**Q.**If the normal at the end of latus rectum of an ellipse x2a2+y2b2=1 of eccentricity e passes through one end of the minor axis then e4+e2=

**Q.**

Which could be the initial point of vector $\text{u}$ if it has a magnitude of $17$ and the terminal point $\left(3,13\right)$$?$

$(-5,-2)$

$(-5,2)$

$(5,-2)$

$(5,2)$

**Q.**The area enclosed by the curve y=9−x2 and the positive coordinate axes is

**Q.**If the area bounded by the curve y=2kx, k>0 and x=0, x=2 and x− axis is 3ln2, then the value of k is

**Q.**If the obtuse angle bisector and angular bisector contains origin is same for the pair of lines 2x+3y−λ=0 and 3x+2y−(λ+2)=0 then λ belongs to

- (−2, 0)
- (−∞, −2)∪(0, ∞)
- (−∞, −2]∪[0, ∞)
- None of the above

**Q.**

In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin.

(a)z = 2 (b)

(c) (d)5*y*
+ 8 = 0

**Q.**The equation of normal at point P(8√2, 1) on the ellipse x2144+y29=1 is

- √2 x+y=15
- √2 x−y=15
- x+√2 y=15
- x−√2 y=15

**Q.**The area bounded by the curve y=1x2 and its asymptote between the lines x=1 to x=3 is

- 13
- 23
- 12
- 16

**Q.**

Column IColumn IIa. If x, y∈R, satisfying the equation (x−4)24+y29=1 p. −23 then the difference between the largest and smallest value of the expression x24+y29 is b. If PQ is focal chord of ellipse x225+y216=1 which passes q. 10through S≡(3, 0) and PS=2, then length of chord PQ isc. If the normal at the point P(θ) to the ellipsex214+y25=1 intersect it again at the point Q(2θ), then the value of cosθ is r. 34√7d. The length of common tangent to x2+y2=16 and s. 89x2+25y2=225 is

- a−s; b−r; c−q; d−p
- a−p; b−q; c−r; d−s
- a−s; b−q; c−p; d−r
- a−q; b−r; c−s; d−p

**Q.**41. Let the line x-2/3=y-1/-5=z+2/2 lie in the plane x+3y-az+b=0 then (a, b) is

**Q.**The slope of the tangent to the curve y=f(x) at (x, f(x)) is 2x+1. lf the curve passes through the point (1, 2) then the area of the re- gion bounded by the curve, the x-axis and the line x=1 is:

- 23
- 13
- 16
- 56

**Q.**The eccentricity of ellipse 4x2+9y2=36 is

- 12√3
- √53
- √56
- 1√3

**Q.**y=x2

^{1/2}- 4a2

^{1/2 }is a normal chord to y

^{2 }= 4ax. Then it’s length is??

**Q.**The locus of the point of intersection of the tangents to the circle x2+y2=a2 at the points whose parametric angle differ by π3 is

- 2(x2+y2)=4a2
- 2(x2+y2)=a2
- 3(x2+y2)=4a2
- 3(x2+y2)=a2

**Q.**Column IColumn IIa. If x, y∈R, satisfying the equation (x−4)24+y29=1 p. −23 then the difference between the largest and smallest value of the expression x24+y29 is b. If PQ is focal chord of ellipse x225+y216=1 which passes q. 10through S≡(3, 0) and PS=2, then length of chord PQ isc. If the normal at the point P(θ) to the ellipsex214+y25=1 intersect it again at the point Q(2θ), then the value of cosθ is r. 34√7d. The length of common tangent to x2+y2=16 and s. 89x2+25y2=225 is

- a−s; b−r; c−q; d−p
- a−p; b−q; c−r; d−s
- a−s; b−q; c−p; d−r
- a−q; b−r; c−s; d−p

**Q.**If the normal at the end of latus rectum of an ellipse x2a2+y2b2=1 of eccentricity e passes through one end of the minor axis then e4+e2=

- 0
- 1
- −1
- 2

**Q.**A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0, 0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is

- x2+y2=8
- x2+y2=34
- x2+y2=64
- x2+y2=15

**Q.**A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0, 0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is

- x2+y2=8
- x2+y2=34
- x2+y2=64
- x2+y2=15

**Q.**A chord MP parallel to the latus rectum of the ellipse x225+y29=1 with centre at O(0, 0) intersects the auxiliary circle at Q. Then the locus of the point of intersection of normals at P and Q to the respective curve is

- x2+y2=8
- x2+y2=34
- x2+y2=64
- x2+y2=15