Question

determine the coordinates of the points where tangents drawn at the points (1 2) and (4 4) to the parabola y2=4x meet

Answer 1

The equation of a tangent to a parabola is

$yy_{1} =2a(x+x_{1} )$

Comparing

y² = 4x with

$y^2=4ax$

We get 4a = 4

a= 1

Now the equation of tangent at (1,2) shall be

y(2) = 2(x+1)

Dividing by 2 on both sides

y= x+1 ......(1)

Equation of tangent at (4,4) shall be

y(4) = 2(x+4)

Dividing by 2 on both sides

2y= x+4 ...(2)

Subtracting (1) from (2) we get

y= 3

Now from (1)

y = x+1

3 = x+1

x=2

The point of intersection is (2,3)

The coordinates of the points where tangents drawn at the points (1 2) and (4 4) to the parabola y²=4x meet are (2,3).

Answer 2

apply T=√S1 and get tangents then equate them..