A tangent to the parabola y2 = 8x makes an angle of 45° with the stra

1.	A tangent to the parabola y2 = 8x makes an angle of 45° with the straight line y = 3x+5. Find theequation of the tangent and its point of contact.3.
Answer» tan45 = \|3 – m\|/\|1 + 3m\| = 1/root2 solvinf for m we get, m = ½. TANGENT OF parabola = > 2ydy/dx = 8 dy/dx = 4/y1 \|let x1 and y1 be the point of contact] m = 4/y1 = ½ y1 = 8. x1 = 64/8 = 8 the eqn. from point of contact (8,8) and slope = ½. (y – 8) = 0.5(x -8) y = x/2 + 4 is the required eqn.

A tangent to the parabola y2 = 8x makes an angle of 45° with the straight line y = 3x+5. Find theequation of the tangent and its point of contact.3.

Answer»

tan45 = |3 – m|/|1 + 3m| = 1/root2

solvinf for m we get, m = ½.

TANGENT OF parabola = > 2ydy/dx = 8

dy/dx = 4/y1 |let x1 and y1 be the point of contact]

m = 4/y1 = ½

y1 = 8.

x1 = 64/8 = 8

the eqn. from point of contact (8,8) and slope = ½.

(y – 8) = 0.5(x -8)

y = x/2 + 4 is the required eqn.