A point on the parabola whose focus is S(1,-1) and whose vertex i… - Vidyadip

MCQ

A point on the parabola whose focus is $S(1,-1)$ and whose vertex is $A(1,1)$ is

✓
$\left(3, \frac{1}{2}\right)$
B
(1, 2)
C
$\left(2, \frac{1}{2}\right)$
D
(2, 2)

✓

Answer

Correct option: A.

$\left(3, \frac{1}{2}\right)$

(A)
Equation of parabola having vertex ( $p, q$ ) and
focus $(p, b+q)$ is given by
$(x-p)^2=4 b(y-q)$
Given, vertex $A=(1,1)$ and focus $S=(1,-1)$
$\therefore p=1, q=1, b=-2$
∴ Equation of parabola is
$(x-1)^2=4(-2)(y-1)$
i.e. $x^2-2 x+8 y-7=0$
Only $\left(3, \frac{1}{2}\right)$ satisfies the above equation of parabola.

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