Question

35. Find the point of intersection of the tangent lines to
the curve y = 2x2 at the points (1, 2) and (-1,2).​

Answer 1

we have to find the point of intersection of the tangent lines to the curve , y = 2x² at the points (1,2) and (-1,2).

Solution : here curve is , y = 2x²

Differentiating with respect to x,

dy/dx = 4x

at (1,2), dy/dx = 4(1) = 4

so, slope of tangent passing through (1,2) is 4

so, equation of tangent is (y - 2) = 4(x - 1)

⇒y - 2 = 4x - 4

⇒4x - y - 2 = 0 ......(1)

at (-1,2) , dy/dx = 4(-1) = -4

slope of tangent passing through (-1,2) is -4.

so equation of tangent is (y - 2) = -4(x +1)

⇒y - 2 = -4x - 4

⇒4x + y + 2 = 0 ......(2)

From equations (1) and (2) we get,

x = 0 and y = -2

So the required point is (0, -2)