The vertex of the parabola x2 + 2y = 8x - 7 is

Question

The vertex of the parabola x2 + 2y = 8x - 7 is (A) ( (9/2), 0) (B) (4, (9/2)) (C) ( 2, (9/2)) (D) ( 4, (7/2))

Tardigrade Admin · Accepted Answer

Given equation of parabola is x2 +2y = 8x -7 ⇒ x2 -8x = -2y -7 ⇒ x2 -8x +16 = -2y -7 +16 ⇒ (x-4)2 = -2(y -(9/2)) ∴ Vertex of the parabola is (4, (9/2))

Q. The vertex of the parabola $x^{2} + 2 y = 8 x - 7$ is

$(\frac{9}{2}, 0)$

$(4, \frac{9}{2})$

$(2, \frac{9}{2})$

$(4, \frac{7}{2})$

Given equation of parabola is

$x^{2} + 2 y = 8 x - 7$

$\Rightarrow x^{2} - 8 x = - 2 y - 7$

$\Rightarrow x^{2} - 8 x + 16 = - 2 y - 7 + 16$

$\Rightarrow (x - 4)^{2} = - 2 (y - \frac{9}{2})$

$∴$ Vertex of the parabola is $(4, \frac{9}{2})$

Q. The vertex of the parabola x2+2y=8x−7 is

(29​,0)

(4,29​)

(2,29​)

(4,27​)