SATHEE: Circle 5 Question 8

Circle 5 Question 8

8. Consider

$\begin{aligned} L_{1} : 2 x + 3 y + p - 3 = 0 \\ L_{2} : 2 x + 3 y + p + 3 = 0 \end{aligned}$

where, $p$ is a real number and

$C : x^{2} + y^{2} - 6 x + 10 y + 30 = 0$

Statement I If line $L_{1}$ is a chord of circle $C$ , then line $L_{2}$ is not always a diameter of circle $C$ .

Statement II If line $L_{1}$ is a diameter of circle $C$ , then line $L_{2}$ is not a chord of circle $C$ .

$(2008, 3 M)$

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Answer:

Correct Answer: 8. (c)

Solution:

Equation of given circle $C$ is

$\begin{array}{ll} (x - 3)^{2} + (y + 5)^{2} = 9 + 25 - 30 \\ i.e. & (x - 3)^{2} + (y + 5)^{2} = 2^{2} \end{array}$

Centre $= (3, - 5)$

If $L_{1}$ is diameter, then $2 (3) + 3 (- 5) + p - 3 = 0 \Rightarrow p = 12$

$∴ \begin{aligned} L_{1} is 2 x + 3 y + 9 & = 0 \\ L_{2} is 2 x + 3 y + 15 & = 0 \end{aligned}$

Distance of centre of circle from $L_{2}$ equals

$| \frac{2 (3) + 3 (- 5) + 15}{\sqrt{2^{2} + 3^{2}}} | = \frac{6}{\sqrt{13}} < 2$

[radius of circle]

$∴ L_{2}$ is a chord of circle $C$ .

Statement II is false.

Circle 5 Question 8

8. Consider

Fill in the Blanks

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Circle 5 Question 8

8. Consider

Fill in the Blanks

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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