Question

If y=2x-3 is a tangent to parabola y2=4a(x-1/3), then a is equal to

Answer 1

Answer:

-14/3

Step-by-step explanation:

Hi,

Given that y = 2x - 3 is a tangent to the parabola y² = 4a(x - 1/3)

Tangent is the line which intersects the given curve at only one point,

If we find the points of intersection of y = 2x - 3 with parabola y² = 4a(x-1/3)

we get,

  (2x - 3)² = 4a(x - 1/3)

=> 4x² -12x - 4ax + 9 + 4a/3 = 0

=>4x² - 4(3+a)x + (9 + 4a/3) = 0

This is a quadratic equation in 'x', but for the given line to be a tangent it should intersect at only one point, hence the above equation should have equal roots.

=>16(3+a)² = 4*4*(9 +4a/3)

=> a² + 6a + 9 = 4a/3 + 9

=> a² + 14a/3 = 0

=> a = 0 or a = -14/3.

But a cannot be 0(then it wouldn't be a parabola)

hence a = -14/3.

Hope, it helped !