IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry - conics-7

Sivvar

If tangents are drawn from a point on x² - 4 y² = 4 to x² + 4 y² = 4 touchin it at Q n R, then mid - point of QR lies on:

(a) (x² - 4 y²)² = 4 (x² + 4 y²)

(b) (x² - 4 y²) = 4 (x² + 4 y²)²

(c) 4(x² - 4 y²) = (x² + 4 y²)²

(d) none of these

how do we approach a prob lik this?? i tried plenty of ways bt i gt stuck after some steps in each method..not able to link all the data..

rhd92781

x^2-4y^2=4 (A conic)
x^2+4y^2=4 (B conic)
frm point (x1, y1) of A, tangents r drawn to B
so eqn of chord of contact will be
xx1+4yy1=4 (i)
let mid point of Q, R be (h, k)
eqn of a chord whose mid point is (h, k) is
T=S1 or hx+4ky-4=h^2+4k^2-4
or hx+4ky=h^2+4k^2 (ii)
compare eqns (i) and (ii), u'll get]
x1/h = y1/k = 4/(h^2+4k^2)
so u get values of x1 n y1 in terms of h, k
this x1, y1 lies on conic A, so satisfy the value of x1, y1 u got in conic A, u'll get the locus of mid-point

rhd92781

if i've not committed a silly mistake, the answer shud be (c)

Sivvar

thnks a lot..ans is right..opt c..

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