Phrases Hyperbola Previous Year Question Paper and Solution with PDF

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Phrases Hyperbola PYQ

Qus : 1Phrases PYQ 2022

If the foci of the ellipse

$\frac{x^2}{25}+\frac{y^2}{b^2}=1$ and the hyperbola

$\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ are coincide, then the value of

$b^2$

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

Solution

Qus : 2Phrases PYQ 2024

At how many points the following curves intersect

$\frac{{y}^2}{9}-\frac{{x}^2}{16}=1$ and

$\frac{{x}^2}{4}+\frac{{(y-4)}^2}{16}=1$

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

Qus : 3Phrases PYQ 2022

${\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1$ ,

$(a{\gt}b)$ and

${x}^2-{y}^2={c}^2$ cut at right angles, then

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Phrases Previous Year PYQPhrases NIMCET 2022 PYQ

Solution

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and

$\frac{x^2}{c^2}+\frac{y^2}{d^2}=1$ are orthogonal.

Then

$a^2-b^2=c^2-d^2$

Similarly

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and

$x^2-y^2=c^2$ are orthogonal.

It means

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and

$\frac{x^2}{c^2}+\frac{y^2}{-c^2}=1$ are orthogonal

Then

$a^2-b^2=c^2-(-c^2)$

$a^2-b^2=2c^2$

Qus : 4Phrases PYQ 2024

If the line

$a^2 x + ay +1=0$ , for some real number

$a$ , is normal to the curve

$xy-=1$ then

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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

Solution

Qus : 5Phrases PYQ 2018

Equation of the common tangents with a positive slope to the circle

and

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Phrases Previous Year PYQPhrases NIMCET 2018 PYQ

Solution

Qus : 6Phrases PYQ 2017

The equation of the hyperbola with centre at the region, length of the transverse axis is 6 and one focus (0, 4) is

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Phrases Previous Year PYQPhrases NIMCET 2017 PYQ

Solution

Qus : 7Phrases PYQ 2015

$3x + 4y + k = 0$ is a tangent to the hyperbola ,

$9x^{2}-16y^{2}=144$ then the value of

$K$ is

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Phrases Previous Year PYQPhrases NIMCET 2015 PYQ

Solution

Qus : 8Phrases PYQ 2023

Find foci of the equation

$x^2 + 2x – 4y^2 + 8y – 7 = 0$

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Phrases Previous Year PYQPhrases NIMCET 2023 PYQ

Solution

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