SATHEE: Circle 1 Question 1

Circle 1 Question 1

1. A circle touching the $X$ -axis at $(3, 0)$ and making a intercept of length 8 on the $Y$ -axis passes through the point

(2019 Main, 12 April II)

(a) $(3, 10)$

(b) $(3, 5)$

(d) $(1, 5)$

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Answer:

Correct Answer: 1. (a)

Solution:

It is given that the circle touches the $X$ -axis at $(3, 0)$ and making an intercept of 8 on the $Y$ -axis.

Let the radius of the circle is ’ $r$ ‘, then the coordinates of centre of circle are $(3, r)$ .

From the figure, we have

$\begin{aligned} C M & = 3, \\ C A & = radius = r \\ and & A M & = B M = \frac{A B}{2} = 4 \\ Then, & r^{2} & = C M^{2} + A M^{2} = 9 + 16 = 25 \\ \Rightarrow & r & = \pm 5 \end{aligned}$

Now, the equation of circle having centre $(3, \pm 5)$ and radius $= 5$ is

$(x - 3)^{2} + (y \pm 5)^{2} = 25$

Now, from the options $(3, 10)$ satisfy the equation of circle

$(x - 3)^{2} + (y - 5)^{2} = 25$

Circle 1 Question 1

1. A circle touching the $X$ -axis at $(3, 0)$ and making a intercept of length 8 on the $Y$ -axis passes through the point

Answer:

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Circle 1 Question 1

1. A circle touching the X-axis at (3,0) and making a intercept of length 8 on the Y-axis passes through the point

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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1. A circle touching the $X$ -axis at $(3, 0)$ and making a intercept of length 8 on the $Y$ -axis passes through the point