Geometry

Circles

Medium

The equation of the circle which passes through the point $(4,5)$ and its centre at $(2,2)$ is

$(x-2)+(y-2)=13$

$(x-2)^{2}+(y-2)^{2}=13$

$x^{2}+y^{2}=13$

$(x-4)^{2}+(y-5)^{2}=13$

✅ Correct Option: 2

The equation of a circle: $(x-a)^{2}+(y-b)^{2}=r^{2}$

With centre of $(a, b)$ and a radius of $r$ .

Only option (2) matches this, hence you can mark the answer right here.

However, here's the rest of the solution:

According to the question, $x=4,y=5$

Go by the options, look at Option 2 and:

$(4-2)^2+(5-2)^2=2^2+3^2=4+9=13 =RHS$

Hence it's the answer.

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Which of the following statements are True in the context of circles?

A. A tangent of a circle touches it at two points.
B. A circle can have two parallel tangents at the most.
C. There is no tangent to a circle passing through a point inside the circle.

Choose the correct answer from the options given below:

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The area of the circle that can be inscribed in a square of side 6 cm is:

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JIPMAT 2021

The radius of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle. BD is tangent to the smaller circle touching it at D. The length AD is.

The equation of the circle which passes through the point (4,5)(4,5)(4,5) and its centre at (2,2)(2,2)(2,2) is

Solution

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JIPMAT Past Year Questions (Topic-Wise)

The equation of the circle which passes through the point $(4,5)$ and its centre at $(2,2)$ is