Question

9. If the join of ends of the latusrectum of x^2= 8y
subtends an angle A°at the vertex of the
parabola then cos A° =​

Answer 1

Given: The join of ends of the latus rectum of x^2= 8y  subtends an angle A°at the vertex of the  parabola.

To find: The value of  cos A?

Solution:

• Now we have given x^2 = 8y.

                  x^2 = 4(2)(y)

• Comparing the above equation with x^2 = 4ay, we get:

                  a = 2

• So focus will be: (0,a) = (0,2)

• Now putting 2 in equation, we get:

                  x^2 = 8(2) = 16

                  x = ±4

• So the points will be:

                  (-4,2) and (4,2)

• Now joining (0,2), (-4,2) and (4,2) with (0,0) a triangle is formed.

• Let A = (4,2), B = (-4,2) and O = (0,0).

• So the distance will be:

                  AB = √(4 - (-4))^2 + (2 - 2)^2

                  AB = √64 = 8 cm

                  OB = √(0 - (-4))^2 + (0 - 2)^2

                  OB = √16 + 4 = √20 = 2√5 cm

                  OA = √(0 - 4)^2 + (0 - 2)^2

                  OA = √16 + 4 = √20 = 2√5 cm

• Now using cosine rule, we get:

                  cos A = (2√5)^2 + (2√5)^2 - (8)^2  / 2 x (2√5) x (2√5)

                  cos A = 20 + 20 - 64 / 40

                  cos A = -24/40

                  cos A = -3/5

Answer:

        So the value of cos A is -3/5.