The one of possible real value of ‘m’ for which the circles, x2 + y2 + 4x + 2(m2 + m) y + 6 = 0 and x2 + y2 + (2y + 1)(m2 + m) = 0 intersect orthogonally is
1) 3
2) -1
3) 2
4) -2
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The one of possible real value of m is -2
Therefore, option (4) is correct.
Explanation:
For circle 1
Comparing this with general equation of circle
....... (1)
Similarly, for circle 2
Comparing this with general equation of circle
......... (2)
We know that the condition that two circles (1) and (2) intersect orthogonally is
Thus,
Let
When
This quadratic equation does not have a real root
Again, taking
Therefore, the one possible real value of m for which the given circles intersect orthogonally is -2
Hope this answer is helpful.
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Q: If the circles x2 + y2 +2x + 2ky + 6 = 0 and x2 + y2 + 2ky + k = 0 intersect orthogonally then k equals ?
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