Question

If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

• A. 3 unit and 4 unit
• B. 6 unit and 4 unit
• C. 3 unit and 8 unit
• D. 6 unit and 8 unit

Answer 1

The correct option is D 6 unit and 8 unit

Solution:

We have, Centre$=(3,4)$ and radius $=5$

Equation of the required circle is

$(x-3{)}^2+(y-4{)}^2=5^2$

For $x-$ intercept,put $y=0$ we get

$(x-3{)}^2+16=25$

or, $(x-3{)}^2=9$

or, $x-3=\pm 3$

or, $x=6$ and $x=0$

Now,

For $y-$ intercept,put $x=0$ we get

$9+(y-4{)}^2=25$

or, $(y-4{)}^2=16$

or, $y-4=\pm 4$

or, $y=8$ and $y=0$

Hence, $x-$intercept is $6$ units and $y-$ intercept is $8$ units.

Hence, D is the correct option.