Options

A. `{:(a,b,c,d),(p,r,q,q):}`
B. `{:(a,b,c,d),(q,p,r,s):}`
C. `{:(a,b,c,d),(s,p,q,r):}`
D. `{:(a,b,c,d),(r,s,q,p):}`

Answer

B

Explanation

2
a. We get common normal perpendicular to y=x.
So, slope `=-1rArrx+y=3a`
b. Tangent to the parabola y=mx+a/m passes through the point P(h,k).
`rArrm^(2)h-mk+a=0`
If its roots are `m_(1)andm_(2)`, then `m_(1)m_(2)-+1`
Thus, locus is x=a.
c. The tangents are
`y=m(x+a)+a//m` (1)
`andy=(-1)/(m)(x+2a)-2am` (2)
Subtracting (1) from (2), we get
x+3a=0
d. If chord joining `t_(1)andt_(1)` subtends angle of `90^(@)` at vertex then `t_(1)t_(2)=-4`. Point of intersection of tangents is `(-at_(1)t_(1),-a(t_(1)+t_(1)))`. So, the locus is x=4a.