TS EAMCET · Maths · Circle
The locus of the centre of the circle touching the \(x\)-axis and passing through the point \((-1,1)\) is
- A a circle with centre at \(\left(-1, \frac{1}{2}\right)\)
- B a pair of lines intersecting at \((-1,1)\)
- C a parabola with focus at \((-1,1)\)
- D a hyperbola with centre at \((-1,1)\)
Answer & Solution
Correct Answer
(C) a parabola with focus at \((-1,1)\)
Step-by-step Solution
Detailed explanation
Let the centre of the circle be \( (x, y) \). Radius \( r = |y| \). \((x - (-1))^2 + (y - 1)^2 = r^2\) \((x + 1)^2 + (y - 1)^2 = y^2\) \((x + 1)^2 + y^2 - 2y + 1 = y^2\) \((x + 1)^2 = 2y - 1\) \((x + 1)^2 = 2\left(y - \frac{1}{2}\right)\) This is a parabola with…
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