Hyperbola is an important topic in the Mathematics section in WBJEE exam. Practising this topic will increase your score overall and make your conceptual grip on WBJEE exam stronger.
This article gives you a full set of WBJEE PYQs for Hyperbola with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Hyperbola questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.
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WBJEE PYQs for Hyperbola with Solutions
1.
Let P be the foot of the perpendicular from focus S of hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ on the line $bx - ay = 0$ and let $C$ be the centre of hyperbola. Then the area of the rectangle whose sides are equal to that of $SP$ and $CP$ is- $2ab$
- $ab$
- $\frac{\left(a^{2}+b^{2}\right)}{2}$
- $\frac{a}{b}$
2.
Let P (4, 3) be a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1.$ If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is- $\frac{\sqrt{5}}{2}$
- $2$
- $\sqrt{2}$
- $\sqrt{3}$
3.
If a hyperbola passes through the point P(\(\sqrt{2},\sqrt{3}\)) and has foci at (±2,0), then the tangent to this hyperbola at P is- y=x\(\sqrt3-\sqrt6\)
\(y = \sqrt{6}x - \sqrt{3}\)
- y=x\(\sqrt6+\sqrt3\)
- y=x\(\sqrt3+\sqrt6\)
4.
The line segment joining the foci of the hyperbola $x^2 - y^2 + 1 = 0$ is one of the diameters of a circle. The equation of the circle is- $x^2 + y^2 = 4$
- $x^{2}+y^{2}=\sqrt{2}$
- $x^2 + y^2 = 2$
- $x^{2}+y^{2}=2\sqrt{2}$
5.
Let $P(3\sec\theta, 2\tan\theta)$ and $Q(3\sec\phi, 2\tan\phi)$ be two points on $\frac{x^2}{9} - \frac{y^2}{4} = 1$ such that $\theta + \phi = \frac{\pi}{2}$. Then the ordinate of the intersection of the normals at $P$ and $Q$ is- 13/2
- -13/2
- 5/2
- -5/2
6.
Let A(2 secθ, 3 tanθ) and B(2 secΦ, 3 tanΦ) where \(\theta+\phi=\frac{\pi}{2}\) be two parts of the hyperbola \(\frac{x^2}{4}-\frac{y^2}{9}=1\). If (α,β) is the point of intersection of normals of the hyperbola at A and B, then β is equal to- \(\frac{12}{3}\)
- \(\frac{13}{3}\)
- \(-\frac{12}{3}\)
\(-\frac{13}{3}\)
7.
If $PQ$ is a double ordinate of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ such that $\Delta OPQ$ is equilateral, $O$ being the centre. Then the eccentricity e satisfies- $1 < e < \frac{2}{\sqrt{3}}$
- $e=\frac{2}{\sqrt{2}}$
- $e=\frac{\sqrt{3}}{2}$
- $e>\frac{2}{\sqrt{3}}$
8.
$PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ such that $\triangle OPQ$ is an equilateral triangle, with $O$ being the center of the hyperbola. Then the eccentricity $e$ of the hyperbola satisfies- 1<e <2/ √3
- e= 2/ √3
- e= 2 √3
- e>2/ √3
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