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NDA Ellipse PYQs with Solutions

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

38 questionsMathematics2010–2026Answers + solutions

About Ellipse PYQs

Ellipse has 38 previous year questions in the Quantrex Academy NDA Mathematics bank. The 38 questions in this list come from NDA (38), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Ellipse PYQs with Solutions

About Ellipse PYQs

Questions by year (this list)

Ellipse questions with solutions

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 α, 5 α) , 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

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

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 (π)/(2) , then what is the eccentricity of the

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?

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