Question

Focus of the parabola ${(y - 2)^2} = 20(x + 3)$ is

$\left( a \right){\text{ }}\left( {3, - 2} \right)$

$\left( b \right){\text{ }}\left( {2, - 3} \right)$

$\left( c \right){\text{ }}\left( {2,2} \right)$

$\left( d \right){\text{ }}\left( {3,3} \right)$

Answer 1

Hint: Compare the given equation of parabola with the standard form and find the values of $x_0$, $y_0$ and a. Substitute these values in focus of parabola $(x_0+a, y_0)$ to find the required solution.

Complete step by step answer:

As, we know that the standard equation of parabola is ${\left( {y - {y_0}} \right)^2} = 4a\left( {x - {x_0}} \right)$. In which,

$\Rightarrow$ Vertex = $(x_0,y_0)$ and,

$\Rightarrow$ Focus of parabola is $(x_0+a, y_0)$

$\Rightarrow {\left( {y - 2} \right)^2} = 20\left( {x + 3} \right)$..............................(1)

Comparing equation (1) with standard equation of parabola we get,

$\Rightarrow {x_0} = - 3,{\text{ }}{y_0} = 2$ and a = 5

So, focus of the parabola in equation 1 will be,

$\Rightarrow {\text{focus}} = \left( { - 3 + 5,2} \right) = \left( {2,2} \right)$

Hence the correct option for the question will be c.

NOTE: - Whenever this type of question is given then compare ${x_0}{\text{, }}{y_0}$ and a with the standard equation of parabola. And then find the required parameter by putting values.