NIMCET Hyperbola Previous Year Question Paper and Solution with PDF

NIMCET Previous Year Questions (PYQs) – Hyperbola – Page 1 of 2

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Qus : 1

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}

Video Solution Discussion

Qus : 2

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

Video Solution Discussion

Qus : 3

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

(a > b)

and

x^{2} - y^{2} = c^{2}

cut at right angles, then

Video Solution Discussion

Qus : 4

If the line

a^{2} x + a y + 1 = 0

, for some real number

a

, is normal to the curve

x y = 1

then

Video Solution Discussion

Qus : 5

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

and

Video Solution Discussion

Qus : 6

Let

F_{1}, F_{2}

be foci of hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

, a>0, b>0, and let O be the origin. Let M be an arbitrary point on curve C and above X-axis and H be a point on

M F_{1}

such that

M F_{2} ⊥ F_{1} F_{2}

M F_{1} ⊥ O H

| O H | = λ | O F_{2} |

with

λ \in (2 / 5, 3 / 5)

, then the range of the eccentricity

e

Video Solution Discussion

Qus : 7

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

Video Solution Discussion

Qus : 8

The locus of the intersection of the two lines

\sqrt{3} x - y = 4 k \sqrt{3}

and

k (\sqrt{3} x + y) = 4 \sqrt{3}

, for different values of k, is a hyperbola. The eccentricity of the hyperbola is:

Video Solution Discussion

Qus : 9

If the foci of the ellipse

b^{2} x^{2} + 16 y^{2} = 16 b^{2}

and the hyperbola

81 x^{2} - 144 y^{2} = \frac{81 \times 144}{25}

coincide, then the value of

b

, is

Video Solution Discussion

Qus : 10

3 x + 4 y + k = 0

is a tangent to the hyperbola ,

9 x^{2} - 16 y^{2} = 144

then the value of

K

Video Solution Discussion

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NIMCET Previous Year Questions (PYQs) – Hyperbola – Page 1 of 2

Solution

Solution

Solution

Solution

Problem:

Step 1: Slope of Line

Step 2: Curve Derivative

Match Slopes

Plug into Curve

✅ Final Answer:

Solution

Solution

Solution

Solution

Solution

Solution

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NIMCET Previous Year Questions (PYQs) – Hyperbola – Page 1 of 2

✓Solution

✓Solution

✓Solution

✓Solution

Problem:

Step 1: Slope of Line

Step 2: Curve Derivative

Match Slopes

Plug into Curve

✅ Final Answer:

✓Solution

✓Solution

✓Solution

✓Solution

✓Solution

✓Solution

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