Orthogonality of Two Circles
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Q.
If a circle passes through the point (a, b) and cuts the circle x2+y2=4 orthogonally, then the locus of its Centre of the circle is _____
2ax + 3by + (a2 + b2 + 4) = 0
2ax + 2by - (a2 + b2 + 4) = 0
2ax - 2by + (a2 + b2 + 4) = 0
2ax - 2by - (a2 + b2 + 4) = 0
Q.
If two circles which pass through the points (0, a) and (0, -a) cut each other orthogonally and touch the straight line y=mx+c, then
c2=a2(1+m2)
c2=a2∣∣1+m2∣∣
c2=2a2(1+m2)
c2=a2(2+m2)
Q. If a circle passes through the point (a, b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is
- 2ax+2by+(a2+b2+4=0)
- 2ax+2by−(a2+b2+4)=0
- 2ax−2by−(a2+b2+4)=0
- 2ax−2by−(a2+b2+4)=0
Q. Which of the following is an incorrect statement.
To prove that PQ = √x,
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1544597/original_21CBSE09MAT01LJ1_Questions.png)
- Mark the centre of the circle as O and join OQ.
- Apply Pythagoras theorem in the triangle OPQ to get PQ = √x.
- Only 1
- Only 2
- Both 1 and 2
- Neither 1 nor 2