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NIMCET Previous Year Questions (PYQs)

NIMCET Hyperbola PYQ

NIMCET PYQ
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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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ
If ${\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1$, $(a{\gt}b)$ and ${x}^2-{y}^2={c}^2$ cut at right angles, then





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

If $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{c^2}+\frac{y^2}{d^2}=1$ are orthogonal.
Then 
$a^2-b^2=c^2-d^2$

Similarly 
If $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ 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 
$a^2-b^2=c^2-(-c^2)$
$a^2-b^2=2c^2$


NIMCET PYQ
Equation of the common tangents with a positive slope to the circle and  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ
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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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ
Find foci of the equation $x^2 + 2x – 4y^2 + 8y – 7 = 0$





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