PYQ Vault
EbooksTutor

Hyperbola with the same foci as a given ellipse

This type of question, asked 5 times: 25 Jul 2022, 31 Jan 2024, 9 Apr 2024, 21 Jan 2026 S1, 28 Jan 2026 S2. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    25 Jul 2022

    164
    Let the foci of the ellipse x216+y27=1\frac{x^{2}}{16}+\frac{y^{2}}{7}= 1 and the hyperbola x2144−y2α=125\frac{x^{2}}{144}-\frac{y^{2}}{\alpha}=\frac{1}{25} coincide. Then the length of the latus rectum of the hyperbola is: -

    Tap an option to check your answer.

  2. Question 2

    31 Jan 2024

    63
    If the foci of a hyperbola are same as that of the ellipse x29+y225=1\frac{x^{2}}{9}+\frac{y^{2}}{25}= 1 and the eccentricity of the hyperbola is 158\frac{15}{8} times the eccentricity of the ellipse, then the smaller focal distance of the point (2,14325)\left( \sqrt{2},\frac{14}{3}\sqrt{\frac{2}{5}} \right) on the hyperbola, is equal to

    Tap an option to check your answer.

  3. Question 3

    9 Apr 2024

    161
    Let the foci of a hyperbola HH coincide with the foci of the ellipse E:(x−1)2100+(y−1)275=1E:\frac{(x- 1)^{2}}{100}+\frac{(y- 1)^{2}}{75}= 1 and the eccentricity of the hyperbola HH be the reciprocal of the eccentricity of the ellipse E. If the length of the transverse axis of HH is α\alpha and the length of its conjugate axis is β\beta, then 3α2+2β23\alpha^{2}+ 2\beta^{2} is equal to:

    Tap an option to check your answer.

  4. Question 4

    21 Jan 2026 S1

    61
    Let the foci of hyperbola coincide with the foci of the ellipse x236+y216=1\frac{x^{2}}{36}+\frac{y^{2}}{16}= 1. If the eccentricity of the hyperbola is 5 , then the length of its latus rectum is:

    Tap an option to check your answer.

  5. Question 5

    28 Jan 2026 S2

    60
    Let the ellipse E:x2144+y2169=1E:\frac{x^{2}}{144}+\frac{y^{2}}{169}= 1 and the hyperbola H:x216−y2λ2=−1H:\frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}= - 1 have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H , then the value of 24(e+L)24(e + L) is :

    Tap an option to check your answer.