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Ellipse — NDA Mathematics PYQs

38 previous year questions from Ellipse with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

Ellipse — NDA Mathematics PYQs

Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the value of p ?

Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the difference between the eccentricities

If any point on an ellipse is (3 , 5 ) , then what is the eccentricity of the ellipse?

The foci of the ellipse 4 x^2+9 y^2=1 are at Q and R . If P (x, y) is any point on the ellipse, then what is PQ + PR equal to?

What is the eccentricity of the ellipse if the angle between the straight lines joining the foci to an extremity of the minor axis is 90^ ?

Paragraph: Consider the following for the next two (02) items that follow: P (x, y) is any point on the ellipse x^2+4 y^2=1 . Let E, F be the foci of the ellipse. Question: What is

Given that 4 x^2+y^2=9 What is the maximum value of y?

Consider the following in respect of the equation x^2 24-k + y^2 k-16 =2 1. The equation represents an ellipse if k =19 . 2. The equation represents a hyperbola if k =12 3. The equ

Paragraph: Consider the following for the next two (02) items that follow: P (x, y) is any point on the ellipse x^2+4 y^2=1 . Let E, F be the foci of the ellipse. Question: Conside

The centre of an ellipse is at (0,0) , major axis is on the y -axis. If the ellipse passes through (3,2) and (1,6) , then what is its eccentricity?

What is the distance between the foci of the ellipse x^2+2 y^2=1 ?

Consider the following with regard to eccentricity (e) of a conic section : 1. e=0 for circle 2. e=1 for parabola 3. e 1 for ellipse Which of the above are correct?

Let P(x, y) be any point on the ellipse 25 x^2+16 y^2=400 . If Q(0,3) and R(0,-3) are two points, then what is (P Q+P R) equal to?

If the angle between the lines joining the end points of minor axis of the ellipse x^2 a^2 + y^2 b^2 =1 with one of its foci is 2 , then what is the eccentricity of the ellipse?

The sum of the focal distances of a point on an ellipse is constant and equal to the

What is the equation of the ellipse whose vertices are ( 5,0) and foci are at ( 4,0) ?

The second degree equation x^2+4 y-2 x-4 y+2=0 represents

The position of the point (1,2) relative to the ellipse 2 x ^2+7 y ^2=20 is

The equation of the ellipse whose centre is at origin, major axis is along x -axis with eccentricity 3 4 and latus rectum 4 units is

What is the equation of the ellipse having foci ( 2,0) and the eccentricity 1 4 ?

A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m . The area of the path

If the ellipse 9 x^2+16 y^2=144 intercepts the line 3 x+4 y=12 , then what is the length of the chord so formed?

Consider any point P on the ellipse x ^2 25 + y ^2 9 =1 in the first quadrant. Let r and s represent its distances from (4,0) and (-4,0) respectively, then (r+s) is equal to

What is the length of the latus rectum of the ellipse 25 x^2+16 y^2=400 ?

What is the sum of the major and minor axes of the ellipse whose eccentricity is 4 / 5 and length of latus rectum is 14.4 unit?

Paragraph : Consider an ellipse x^2 a^2 + y^2 b^2 =1 Question : What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?

The length of latus rectum of the ellipse 4 x^2+9 y^2=36 is

The equation of the ellipse whose vertices are at ( 5,0) and foci at ( 4,0) is

The sum of the focal distances of a point on the ellipse x^2 4 + y^2 9 =1 is :

The eccentricity e of an ellipse satisfies the condition:

What is the eccentricity of the conic 4 x^2+9 y^2=144 ?

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?

What is the sum of the focal distances of a point of an ellipse x^2 a^2 + y^2 b^2 =1 ?

What are the equations of the directrices of the ellipse 25 x^2+16 y^2=400 ?

If the latus rectum of an ellipse is equal to half its minor axis, then what is its eccentricity?

A point P moves such that the difference of its distances from two given points (c, 0) and (-c, 0) is constant. What is the locus of the point P ?

If (4,0) and (-4,0) are the foci of an ellipse and the semi-minor axis is 3 ; then the ellipse passes through which one of the following points?

A circle is drawn with the two foci of an ellipse x^2 a^2 + y^2 b^2 =1 at the end of the diameter. What is the equation to the circle?