SATHEE: Circle 1 Question 12

Circle 1 Question 12

12. Circle(s) touching $X$ -axis at a distance 3 from the origin and having an intercept of length $2 \sqrt{7}$ on $Y$ -axis is/are

(a) $x^{2} + y^{2} - 6 x + 8 y + 9 = 0$

(2013 Adv.)

(b) $x^{2} + y^{2} - 6 x + 7 y + 9 = 0$

(d) $x^{2} + y^{2} - 6 x - 7 y + 9 = 0$

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Answer:

Correct Answer: 12. (a , c)

Solution:

PLAN

Here, the length of intercept on $Y$ -axis is $\Rightarrow 2 \sqrt{f^{2} - c}$ and if circle touches $X$ -axis

passes through $(3, 0)$ .

$\begin{aligned} \Rightarrow 9 + 6 g + c = 0 \\ \begin{aligned} g^{2} & = c \\ 2 \sqrt{f^{2} - c} & = 2 \sqrt{7} \end{aligned} \\ f^{2} - c = 7 \end{aligned}$

From Eqs. (i) and (ii), we get

$\begin{aligned} g^{2} + 6 g + 9 & = 0 \Rightarrow (g + 3)^{2} = 0 \\ \Rightarrow & g & = - 3 and c = 9 \\ ∴ & f^{2} & = 16 \Rightarrow f = \pm 4 \\ ∴ & x^{2} + y^{2} - 6 x \pm 8 y + 9 & = 0 \end{aligned}$

Circle 1 Question 12

12. Circle(s) touching $X$ -axis at a distance 3 from the origin and having an intercept of length $2 \sqrt{7}$ on $Y$ -axis is/are

Answer:

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Circle 1 Question 12

12. Circle(s) touching X-axis at a distance 3 from the origin and having an intercept of length 27 on Y-axis is/are

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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12. Circle(s) touching $X$ -axis at a distance 3 from the origin and having an intercept of length $2 \sqrt{7}$ on $Y$ -axis is/are