Question

12.Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis.

Answer 1

Given, vertex of parabola is ( 0,0 ) and parabola is symmetric about y axis and passes through (5,2)

Since the parabola is symmetric about y axis, the equation of the parabola is either x 2 =4ay or x 2 =−4ay

Parabola passes through the point (5,2) which lies in first quadrant so parabola is of the form x 2 =4ay (1)

Since (5,2) passes through parabola, it satisfies the equation of the parabola given in (1),

x 2 =4ay 5 2 =4×a×2 a= 25 8

Substitute the value of a in equation (1)

x 2 =4ay x 2 =4× 25 8 ×y x 2 = 25 2 ×y 2 x 2 =25y

Thus, the equation of the parabola with vertex (0,0) and passes through (5,2) and has symmetry about y axis as 2 x 2 =25y .