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Yukti Vault

Coordinate Geometry

Hyperbola: JEE Main & Advanced PYQs

112 previous year questions on Hyperbola from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

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Questions 101-112 of 112

  1. The line $2x+y=1$ is tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If this line passes through the point of intersection of the nearest directrix and the …
  2. Consider the hyperbola $H:x^2-y^2=1$ and a circle $S$ with center $N(x_2,0)$. Suppose that $H$ and $S$ touch each other at a point $P(x_1,y_1)$ with $x_1>1$ and $y_1>0$. …
  3. Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $a>b>0$, be a hyperbola in the $xy$-plane whose conjugate axis $LM$ subtends an angle of $60^0$ at one of its vertices …
  4. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
  5. The locus of the midpoints of the chord of the circle, $x^{2}+y^{2}=25$ which is tangent to the hyperbola, $\dfrac{x^{2}}{9}-\dfrac{y^{2}}{16}=1$ is :
  6. Consider a hyperbola $H$ having centre at the origin and foci on the $x$-axis. Let $C_1$ be the circle touching the hyperbola $H$ and having the centre at the origin. …
  7. If the line $y=mx+c$ is a common tangent to the hyperbola $\dfrac{x^{2}}{100}-\dfrac{y^{2}}{64}=1$ and the circle $x^{2}+y^{2}=36$, then which one of the following is …
  8. Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is :
  9. Let the circle $C$ touch the line $x-y+1=0$, have the centre on the positive $x$-axis, and cut off a chord of length $\dfrac{4}{\sqrt{13}}$ along the line $-3x+2y=1$. …
  10. Let $H_1:\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$ and $H_2:-\dfrac{x^{2}}{A^{2}}+\dfrac{y^{2}}{B^{2}}=1$ be two hyperbolas having length of latus rectums …
  11. If $A$ and $B$ are the points of intersection of the circle $x^{2}+y^{2}-8x=0$ and the hyperbola $\dfrac{x^{2}}{9}-\dfrac{y^{2}}{4}=1$ and a point $P$ moves on the line …
  12. The locus of a point $P(\alpha,\beta)$ moving under the condition that the line $y=\alpha x+\beta$ is tangent to the hyperbola …

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