JEE Main 2018 (Offline) | Hyperbola Question 65 | Mathematics

Tangents are drawn to the hyperbola 4x² - y² = 36 at the points P and Q.

If these tangents intersect at the point T(0, 3) then the area (in sq. units) of $$\Delta $$PTQ is :

$$36\sqrt 5 $$

$$45\sqrt 5 $$

$$54\sqrt 3 $$

$$60\sqrt 3 $$

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MCQ (Single Correct Answer)

-1

Out of Syllabus

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

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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

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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