SATHEE: Circle 3 Question 15

Circle 3 Question 15

15. The equation of circle $C$ is

(a) $(x - 2 \sqrt{3})^{2} + (y - 1)^{2} = 1$

(b) $(x - 2 \sqrt{3})^{2} + y + {\frac{1}{2}}^{2} = 1$

(d) $(x - \sqrt{3})^{2} + (y - 1)^{2} = 1$

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Answer:

Correct Answer: 15. (d)

Solution:

Let centre of circle $C$ be $(h, k)$ .

$\begin{aligned} Then, \\ | \frac{\sqrt{3} h + k - 6}{\sqrt{3 + 1}} | = 1 \\ \begin{array}{lc} \Rightarrow & \sqrt{3} h + k - 6 = 2, - 2 \\ \Rightarrow & \sqrt{3} h + k = 4 \end{array} \end{aligned}$

[rejecting 2 because origin and centre of $C$ are on the same side of $P Q$ ] The point $(\sqrt{3}, 1)$ satisfies Eq. (i).

$∴$ Equation of circle $C$ is $(x - \sqrt{3})^{2} + (y - 1)^{2} = 1$ .

Clearly, points $E$ and $F$ satisfy the equations given in option (d).

Circle 3 Question 15

15. The equation of circle $C$ is

Answer:

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Circle 3 Question 15

15. The equation of circle C is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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15. The equation of circle $C$ is