The parabolas C_1:y^2=4ax-a and C_2:y^2=-4ax-k intersect at two distinct points A and B. If the slope of the tangent at A on C_1 is same as the slope…

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The parabolas C_1:y^2=4ax-a and C_2:y^2=-4ax-k intersect at two distinct points A and B. If the slope of the tangent at A on C_1 is same as the slope of the normal at B on C_2 , then the value of k is equal to

MARKS Content Team · Accepted Answer

Correct answer: (A) 3a. Let, A=p,q & B=p,-q Now q^2=4ap-a & q^2=-4ap-k …(i) ⇒p-a=-p+k⇒p=(a+k)/2 …(ii) Now for C_1, dy/dx=2a/y dy_(dxp,q)=2a/q & -dxdy_(p,-q)=q/2a ⇒ 2a/q=q/2a⇒q^2=4a^2 … (iii) Putting values from (ii) & (iii) in equation (i), we get, 4a^2=4a(a+k)/2-a ⇒a=(k-a)/2⇒k=3a

The parabolas $C_{1} : y^{2} = 4 a (x - a)$ and $C_{2} : y^{2} = - 4 a (x - k)$ intersect at two distinct points $A$ and $B .$ If the slope of the tangent at $A$ on $C_{1}$ is same as the slope of the normal at $B$ on $C_{2}$ , then the value of k is equal to

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More Parabola Questions

The parabolas C1:y2=4ax-a and C2:y2=-4ax-k intersect at two distinct points A and B. If the slope of the tangent at A on C1 is same as the slope of the normal at B on C2 , then the value of k is equal to

Solution

More Parabola Questions

The parabolas $C_{1} : y^{2} = 4 a (x - a)$ and $C_{2} : y^{2} = - 4 a (x - k)$ intersect at two distinct points $A$ and $B .$ If the slope of the tangent at $A$ on $C_{1}$ is same as the slope of the normal at $B$ on $C_{2}$ , then the value of k is equal to