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The equations of the common tangents to the parabola `y = x^2 and y=-(x-2)^2` is/are :A. y=4(x-1)B. y=0C. y=-4(x-1)D. y=-30x-50 |
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Answer» Correct Answer - A::B 1,2 If y=mx+c is tangent to `y=x^(2)`, then `x^(2)-mx-c=0` has equal root. So, `m^(2)+4c=0` `orc=-(m^(2))/(4)` So, the tangent to `y=x^(2)` is `y=mx-(m^(2))/(4)` Since this is also tangent to `y=-(x-2)^(2)`, `mx-(m^(2))/(4)=-x^(2)+4x-4` has equal roots. So, `x^(2)+(m-4)x+(4-(m^(2))/(4))=0` has equal roots. So, `(m-4)^(2)-4(4-(m^(2))/(4))=0` `orm^(2)=8m+16+m^(2)-16=0` `orm=0,4` So,, y=0 and y=4x-4 is the tangent. |
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