1.

Match the following lists:

Answer»


Solution :
(a) OBVIOUSLY, all the points in List II are common to the hyperbola and circle.
(b). The chord of contact of hyperbola w.r.t. (0, -9/4) is
`0(x)-(-(9)/(4))y=9`
`"or"y=4`
Solving this with hyperbola, we have
`x^(2)-16=9`
`"or"x^(2)=25or x= pm5`
Hence, the point of contact are `(pm 5, 4)`.
(c) Obviously, the required point is `(-5, -4)`.
(d) LET the point on the hyperbola be P(H,k) and `Q(-h,k)`. Then
`"Area of TRIANGLE"=(1)/(2)|2h||-6-k|=10"(1)"`
Also, points P and Q lie on the hyperbola. Hence,
`h^(2)-k^(2)=9"(2)"`
Clearly, point `(pm5,-4)` satisfy both (1) and (2).


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