CircleHard
Question
If the tangent at the P on the circle x2 + y2 + 2x + 2y = 7 meets the straight line 3x - 4y = 15 at a point Q on the x+axis, then length of PQ is
Options
A.3√7
B.4√7
C.2√7
D.√7
Solution
Let P be (x1, y1) and Q be (h, 0). Equation of tangent at (x1y1) is
xx1 + yy1 +1 x + x1 + 1 y + y1 - 7 = 0.
This passes through (h, 0)
∴ hx1 + (h + x1) + y1 - 7 = 0 .......(1)
Now (h, 0) also lies on 3x - 4y = 15
∴ 3h - 0 = 15 ⇒ h = 5
We know length of tangent = √S1
Here, Q is (5, 0)
So, length of tangent =
= 
= 
xx1 + yy1 +1 x + x1 + 1 y + y1 - 7 = 0.
This passes through (h, 0)
∴ hx1 + (h + x1) + y1 - 7 = 0 .......(1)
Now (h, 0) also lies on 3x - 4y = 15
∴ 3h - 0 = 15 ⇒ h = 5
We know length of tangent = √S1
Here, Q is (5, 0)
So, length of tangent =
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