Test Index

Circle

Section: Mathematics

© examsnet.com

Question : 31 of 89

Marks: +1, -0

If

(a, b)

is the common point for the circles

x^2+y^2-4 x+4 y-1=0

x^2+y^2+2 x-4 y+1=0

a^2+b^2=

[AP EAPCET 21 May 2025 S2]

$\;\frac{1}{5}$
$5$
$25$
$\;\frac{1}{25}$

Solution:

(a, b)

is the common point for the two given circle

\;a^2+b^2-4 a+4 b-1=0 ....(i)

\;a^2+b^2+2 a-4 b+1=0 .....(ii)

Subtrating Eqs. (ii)form(i), we get

\;-6 a+8 b-2=0

\;-3 a+4 b-1=0

\;4 b=3 a+1 .....(iii)

From Eqs. (i) and (iii), we get

\;a^2+ \left(\frac{3 a+1}{4}\right)^2 -4 a+3 a+1-1=0

\;\Rightarrow 25 a^2-10 a+1=0

\;\;\; (5 a-1)^2=0

\;\;\; a=\;\frac{1}{5} \;\text{ and }\; b=\;\frac{2}{5}

Now,

a^2+b^2=\;\frac{1}{25}+\;\frac{4}{25}=\;\frac{5}{25}=\;\frac{1}{5}

© examsnet.com

Go to Question:

Prev Question

Next Question