1
IIT-JEE 2002
MCQ (Single Correct Answer)
+4
-1
If the pair of lines $$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$ intersect on the $$y$$ axis then
A
$$2fgh = b{g^2} + c{h^2}$$
B
$$b{g^2} \ne c{h^2}$$
C
$$\,abc = 2fgh$$
D
none of these
2
IIT-JEE 2002
MCQ (Single Correct Answer)
+4
-1
The pair of lines represented by
$$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$ are perpendicular to each other for
A
two values of $$a$$
B
$$\forall \,a$$
C
for one values of $$a$$
D
for no values of $$a$$
3
IIT-JEE 2002
Subjective
+5
-0
Prove that, in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.
4
IIT-JEE 2002
Subjective
+5
-0
Prove that $$\cos \,ta{n^{ - 1}}\sin \,{\cot ^{ - 1}}x = \sqrt {{{{x^2} + 1} \over {{x^2} + 2}}} $$.
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