NIMCET 2023 Question Paper with solutions

Question : 20 of 120

Marks: +1, -0

The foci of the graph represented by

x^2-4 y^2

+2 x+8 y-7=0

is:

Solution:

(x^2+2 x+1) -4 (y^2-2 y) =7+1

\;⇒ \;\; (x+1)^2-4(y-1)^2=4

\;⇒ \;\; \;{(x+1)^2}/{4}-\;{(y-1)^2}/{1}=1

Hence, center is

(-1,1)

⇒\;b^2\;=a^2 (e^2-1)

⇒ 1\;=4 (e^2-1)

⇒ e\;=\;{{√{5}}}/{2}

⇒ a e\;=\;{{√{5}}}/{2} × 2

focii are at a distance are from center.
Hence, focii will be

(-1+{√{5}}, 1)

(-1-{√{5}}, 1)

Go to Question:

Prev Question

Next Question