# Directrix of Ellipse

## Trending Questions

**Q.**The equation of the ellipse with vertices (±13, 0) and foci (±5, 0), is

- x2169+y2144=1
- x213+y212=1
- x213+y211=1
- x2169+y2121=1

**Q.**

If the distance between the directrices of a rectangular hyperbola are $10$, then the distance between its foci will be

$10\sqrt{2}$

$5$

$5\sqrt{2}$

$20$

**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.

The orthocentre of the triangle F1MN is

- (23, 0)
- (910, 0)
- (23, √6)
- (−910, 0)

**Q.**Let the normals at the four points (x1, y1), (x2, y2), (x3, y3) and (x4, y4) on the ellipse x2a2+y2b2=1 be concurrent at some point (called as conormal point). Then (x1+x2+x3+x4)(1x1+1x2+1x3+1x4) is equal to

- 4
- 3
- −4
- 2

**Q.**If the distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is

- 12
- 23
- 1√3
- 45

**Q.**The equation of the ellipse with foci at (±5, 0) and x=365 as one directrix, is

- x211+y236=1
- x236+y29=1
- x29+y236=1
- x236+y211=1

**Q.**

If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 12 , then length of the minor axis is

3

6

None of these

**Q.**The foci of the ellipse, 25(x+1)2+9(y+2)2=225 are

- (−1, 2) and (−1, −6)
- (−1, −2) and (−1, −6)
- (−2, 1) and (−2, 6)
- (−1, −2) and (−2, −1)

**Q.**The equation of the directrix of the ellipse x225+y29=1 is/are

- y=254
- y=−254
- x=−254
- x=254

**Q.**The latus rectum subtends a right angle at the centre of the ellipse, then its eccentricity is

- 2sin18∘
- 2cos18∘
- 2sin54∘
- 2cos54∘

**Q.**Let the normals at the four points (x1, y1), (x2, y2), (x3, y3) and (x4, y4) on the ellipse x2a2+y2b2=1 be concurrent at some point (called as conormal point). Then (x1+x2+x3+x4)(1x1+1x2+1x3+1x4) is equal to

- 4
- 3
- −4
- 2

**Q.**A set of lines x+y−2+λ(2x+y−3)=0 represents incident rays on an ellipse S=0 and

2x+3y−23+μ(2x−y−3)=0 represents the set of reflected rays from the ellipse where λ, μ∈R. If P(3, 7) is a point on the ellipse normal at which meets the major axis at N then

- Eccentricity of ellipse is √52√2+1
- N divides line segment joining two foci in the ratio 2√2:1
- Area of triangle formed by point P and two foci is 5 Sq. unit.
- Eccentricity of ellipse is √52√2−1

**Q.**The radius of the circle passing through the point of intersection of ellipse x2a2+y2b2=1 and x2−y2=0

- √2ab√a2+b2 unit
- a2+b2√a2−b2 unit
- a2−b2√a2+b2 unit
- ab√a2+b2 unit

**Q.**

If $\mathrm{\xce\xbb}(3i+2j-6k)$ is a unit vector, then the values of $\mathrm{\xce\xbb}$ are:

$\xc2\pm \frac{1}{7}$

$\xc2\pm 7$

$\xc2\pm \sqrt{43}$

$\xc2\pm \frac{1}{\sqrt{43}}$

$\xc2\pm \frac{1}{\sqrt{7}}$

**Q.**

Let the ellipse C1:x2a21+y2b21=1 (a1>b1) and the hyperbola C2:x2a22−y2b22=1 have the same focus point F1 and F2. If point P is the intersection point of C1 and C2 in the first quadrant and |F1F2|=2|PF2|, then which of the following is (are) CORRECT?

( e1 and e2 are eccentricities of ellipse and hyperbola respectively.)

- e1∈(12, 1)
- e2−e1∈(12, ∞)
- e1∈(14, 12)
- e2+e1∈(32, ∞)

**Q.**

The equation of the ellipse whose foci are ( Â±5 , 0 ) and one of its dierctrix is 5x = 36 , is

None of these

**Q.**For the ellipse x2+3y2+2x−12y+10=0, which of the following option(s) is/are correct

- centre is (−1, 2)
- length of the axes are 2√3 and 2 units
- eccentricity is √23
- length of latus ractum is 2√3 units

**Q.**

If (−7−24i)1/2=x-iy, then x2+y2=

25

-25

None of these

15

**Q.**Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3, ...} of rectangles as follows:

E1:x29+y24=1;

R1: rectangle of largest area, with sides parallel to the axes, inscribed in E1;

En: ellipse x2a2n+y2b2n=1 of largest area inscribed in Rn−1, n>1;

Rn: rectangle of largest area, with sides parallel to the axes, inscribed in En, n>1;

Then which of the following option is/are correct?

- The eccentricities of E18 and E19 are NOT equal
- N∑n=1(area of Rn)<24, for each positive integers N
- The length of latus rectum of E9 is 16
- The distance of a focus from the centre in E9 is √532

**Q.**Let f:R→R be a continuous function satisfying

f(x)+x∫0tf(t)dt+x2=0, for all x∈R. Then

- limx→∞f(x)=2
- limx→∞f(x)=−2
- f(x) has more than one point in common with the x−axis
- f(x) is an odd function

**Q.**Let S1, S2 are foci of an ellipse, whose major axis length is 15 units and P be any point on the ellipse such that perimeter of triangle PS1S2 is 20 units. If e is the eccentricity of the ellipse, then 3e=

**Q.**If the extremities of the latus rectum of the ellipse x225+y216=1 is (α, β), then the distance between the point P(1, 1) and (α, β), when α>0 is/are

- √22125 units
- √2215 units
- √5415 units
- √54125 units

**Q.**If the minor axis of an ellipse subtends an angle of 60∘ at each focus of the ellipse, then 4e2=

(where e is eccentricity)

**Q.**If the least distance between a point on x2+2y2=6 and x+y−7=0 is k√2 unit, then k=

**Q.**The equation of the axes of the ellipse 4x2+3y2−8x+6y−5=0, are

- major axis is y+1=0
- minor axis is y+1=0
- minor axis is x=1
- major axis is x=1

**Q.**The relation is a subset of on the power set P(A) of a set A is ?

- Symmetric
- Anti-symmetric
- Equivalence relation
- Transitive

**Q.**A rectangle ABCD has area 200.Sq.units and an ellipse with area 200π Sq.units having foci at B and D passes through A and C . If the perimeter of the rectangle is P units then the value of P20 is

**Q.**Give an example of a relation which is symmetric and transitive but not reflexive

**Q.**If the points of intersection of the circle x2+y2=16 with x−axis are foci of an ellipse and points of intersection of circle x2+y2=16 with y−axis are end points of minor axis of the same ellipse, then eccentricity of the ellipse is

- 12√2
- 12
- 1√2
- 13√2

**Q.**An ellipse having co-ordinate axes as its axes having lengths 2a and 2b units respectively, Where a and b are middle terms of a series a1, a2, a3⋯a10, aia11−i=5√3 ∀ i∈N, i<11. If B, F, F′ are one end of minor axis and foci of the ellipse respectively, such that triangle FBF′ is an equilateral triangle, then equation of ellipse is

- x210+2y215=1
- x215+y25=1
- x210+y215=1
- 2x215+y210=1