JEE Mains · Maths · STD 11 - 12. limits
Let a circle passing through \((2,0)\) have its centre at the point \((\mathrm{h}, \mathrm{k})\). Let \(\left(\mathrm{x}_{\mathrm{c}}, \mathrm{y}_{\mathrm{c}}\right)\) be the point of intersection of the lines \(3 x+5 y=1\) and \((2+c) x+\) \(5 c^2 y=1\). If \(h=\lim _{c \rightarrow 1} x_c\) and \(k=\lim _{c \rightarrow 1} y_c\), then the equation of the circle is :
- A \(25 x^2+25 y^2-20 x+2 y-60=0\)
- B \(5 x^2+5 y^2-4 x-2 y-12=0\)
- C \(25 x^2+25 y^2-2 x+2 y-60=0\)
- D \(5 x^2+5 y^2-4 x+2 y-12=0\)
Answer & Solution
Correct Answer
(A) \(25 x^2+25 y^2-20 x+2 y-60=0\)
Step-by-step Solution
Detailed explanation
\( (2+c) x+5 c^2\left(\frac{1-3 x}{5}\right)=1 \) \( \mathrm{x}=\frac{1-\mathrm{c}^2}{2+\mathrm{c}-3 \mathrm{c}^2}, \mathrm{y}=\frac{1-3 \mathrm{x}}{5}=\frac{\mathrm{c}-1}{5\left(2+\mathrm{c}-3 \mathrm{c}^2\right)} \)…
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