Question bank/JEE Main/Mathematics

JEE MainMathematicsModerateCircles

If circles x2+y2+2gx+2y+2=0x^{2} + y^{2} + 2gx + 2y + 2 = 0 and
x2+y2+2x+2fy+4=0x^{2} + y^{2} + 2x + 2fy + 4 = 0 intersect in two distinct points P
and Q. and equation of line PQ is x+y+1=0x + y + 1 = 0 then find the value of
g + f.;fn o`Ùk x2+y2+2gx+2y+2=0x^{2} + y^{2} + 2gx + 2y + 2 = 0,oa
x2+y2+2x+2fy+4=0x^{2} + y^{2} + 2x + 2fy + 4 = 0 ijLij nks fHkUu & fHkUu fcUnqvksa P
rks g + f

Show answer and solution
Equation of PQ is S1−S2=0S_{1} - S_{2} = 0
PQ dk lehdj.k S1−S2=0S_{1} - S_{2} = 0
2x(g−1)+2y(1−f)−2=02x(g - 1) + 2y(1 - f) - 2 = 0
Given equation of PQ is x+y+1=0x + y + 1 = 0
Now by comparing nksuksa dh rqyuk djus ij
g−11=1−f1=−11∴g=0,f=2\frac{g - 1}{1} = \frac{1 - f}{1} = \frac{- 1}{1}\therefore g = 0,f = 2.

Source: Grass-G / M-25 Mathematics Paper 7 Jan.docx

More JEE Main questionsChapter practice

Need a video for this idea?

Scan any doubt from your notes and get a whiteboard explanation.

Scan a doubtView plans