Saved Bookmarks
| 1. |
The equation of the line touching both the parabolas `y^(2)=4xandx^(2)=-32y` is ax+by+c=0. Then the value of a+b+c is ___________ . |
|
Answer» Correct Answer - 3 (3) The equation of tangent to parabola `y^(2)=4x` is `y=mx+(1)/(m)` Since (1) is also the tangent of `x^(2)=-32y`, we have `x^(2)=-32(mx+(1)/(m))` `orx^(2)+32mx+(32)/(m)=0` The above equation must have equal roots. Hence, its discriminant must be zero. Therefore, `(32m)^(2)=4xx1xx(32)/(m)` `i.e.," "m^(3)=(1)/(8)or=(1)/(2)` From (1), `y=(x)/(2)+2` `orx-2y+4=0` |
|