In the xy-plane, two circles C and R are drawn such that Circle C has its center at the origin and radius equal to 5 and Circle R has its center at (2, 3) and radius equal to 5. Which of the following is the equation of the line that passes through the intersection points of circles C and R?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer?

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In the xy-plane, two circles C and R are drawn such that Circle C has its center at the origin and radius equal to 5 and Circle R has its center at (2, 3) and radius equal to 5. Which of the following is the equation of the line that passes through the intersection points of circles C and R?

Correct answer is option 'D'. Can you explain this answer?

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In the xy-plane, two circles C and R are drawn such that Circle C has ...

Circle R
- Origin = (2, 3)
- Radius = 5
- Now, all the points that lie on the Circle R will be at a distance of 5

units (i.e. the radius) from the centre of the circle(2, 3)

To Find: The equation of the line that passes through the intersection point of Circle C and R?

Approach:

To find the equation of a line that passes through the intersection points of Circles C and R, we need to find two points that lie on the line.

As the line passes through the two intersection points of the circles C and R, the equation of the line will satisfy these two intersection points.

Also the two intersection points of the circles should satisfy the equation of all the points lying on both the circles.

So, we can equate the equations of the points lying on circle C and R to find the equation of the line passing through the intersection points.

Working out:

Equation of all the points lying on Circle C:
Equation of all the points lying on Circle R:
Equating both the equations, will give us the equation of the line that passes these intersection points:

Thus, the line segment that passes through the intersection points of Circle C
and R should have itsequation as

Answer: D

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