Saved Bookmarks
| 1. |
If two tangents drawn from the point `(alpha,beta)`to the parabola `y^2=4x`are such that the slope of one tangent is double of the other, thenprove that `alpha=2/9beta^2dot` |
|
Answer» Tangent to the parabola `y^(2)=4x` having slope m is `y=mx+(1)/(m)` It passes through `(alpha,beta)`. Therefore, `beta=malpha+(1)/(m)` `oralpham^(2)-betam+1=0` According to the question, it has roots `m_(1)and2m_(1)`. Now, `m_(1)+2m_(1)=(beta)/(alpha)andm_(1)*2m_(1)=(1)/(alpha)` `or2((beta)/(3alpha))^(2)=(1)/(alpha)` `oralpha=(2)/(9)beta^(2)` |
|