JEE Main 2018 (Online) 15th April Evening Slot | Hyperbola Question 66 | Mathematics

A normal to the hyperbola, 4x² $$-$$ 9y² = 36 meets the co-ordinate axes $$x$$ and y at A and B, respectively. If the parallelogram OABP (O being the origin) is formed, then the ocus of P is :

4x² + 9y² = 121

9x² + 4y² = 169

4x² $$-$$ 9y² = 121

9x² $$-$$ 4y² = 169

JEE Main 2018 (Online) 15th April Morning Slot

MCQ (Single Correct Answer)

-1

If the tangents drawn to the hyperbola 4y² = x² + 1 intersect the co-ordinate axes at the distinct points A and B then the locus of the mid point of AB is :

x² $$-$$ 4y² + 16x²y² = 0

x² $$-$$ 4y² $$-$$ 16x²y² = 0

4x² $$-$$ y² + 16x²y² = 0

4x² $$-$$ y² $$-$$ 16x²y² = 0

JEE Main 2017 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

The locus of the point of intersection of the straight lines,

tx $$-$$ 2y $$-$$ 3t = 0

x $$-$$ 2ty + 3 = 0 (t $$ \in $$ R), is :

an ellipse with eccentricity $${2 \over {\sqrt 5 }}$$

an ellipse with the length of major axis 6

a hyperbola with eccentricity $$\sqrt 5 $$

a hyperbola with the length of conjugate axis 3

JEE Main 2017 (Offline)

MCQ (Single Correct Answer)

-1

Out of Syllabus

A hyperbola passes through the point P$$\left( {\sqrt 2 ,\sqrt 3 } \right)$$ and has foci at $$\left( { \pm 2,0} \right)$$. Then the tangent to this hyperbola at P also passes through the point :

$$\left( {2\sqrt 2 ,3\sqrt 3 } \right)$$

$$\left( {\sqrt 3 ,\sqrt 2 } \right)$$

$$\left( { - \sqrt 2 , - \sqrt 3 } \right)$$

$$\left( {3\sqrt 2 ,2\sqrt 3 } \right)$$

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