AP EAMCET · Maths · Parabola
The centre of the circle that passes through the point \((0,1)\) and touches the curve \(y=x^2\) at \((2,4)\) is
- A \(\left(\frac{-16}{5}, \frac{27}{10}\right)\)
- B \(\left(\frac{-16}{7}, \frac{53}{10}\right)\)
- C \(\left(\frac{-16}{5}, \frac{53}{10}\right)\)
- D \(\left(\frac{-16}{5}, \frac{-53}{10}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{-16}{5}, \frac{53}{10}\right)\)
Step-by-step Solution
Detailed explanation
Let equation of circle is \(x^2+y^2+2 g x+2 f y+c=0\) Where centre is \((-\mathrm{g},-\mathrm{f})\) Since circle passes through \((0,1)\) \[ \Rightarrow 0+1+0+2 \mathrm{f}+\mathrm{c}=0 \Rightarrow \mathrm{c}=2 \mathrm{f}-1 \] \((2,4)\) is also on the circle.…
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