SATHEE: Circle 1 Question 9

Circle 1 Question 9

9. The lines $2 x - 3 y = 5$ and $3 x - 4 y = 7$ are diameters of a circle of area $154 s q$ units. Then, the equation of this circle is

$(1989, 2 M)$

(a) $x^{2} + y^{2} + 2 x - 2 y = 62$

(b) $x^{2} + y^{2} + 2 x - 2 y = 47$

(d) $x^{2} + y^{2} - 2 x + 2 y = 62$

Show Answer

Answer:

Correct Answer: 9. (c)

Solution:

Since, $2 x - 3 y = 5$ and $3 x - 4 y = 7$ are diameters of a circle.

Their point of intersection is centre $(1, - 1)$ .

Also given,

$π r^{2} = 154$

$\Rightarrow r^{2} = 154 \times \frac{7}{22} \Rightarrow r = 7$

$∴$ Required equation of circle is

$\begin{array}{ll} (x - 1)^{2} + (y + 1)^{2} = 7^{2} \\ \Rightarrow & x^{2} + y^{2} - 2 x + 2 y = 47 \end{array}$

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Circle 1 Question 9

9. The lines 2x−3y=5 and 3x−4y=7 are diameters of a circle of area 154sq units. Then, the equation of this circle is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

9. The lines $2 x - 3 y = 5$ and $3 x - 4 y = 7$ are diameters of a circle of area $154 s q$ units. Then, the equation of this circle is