wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A circle touching the x-axis at (3,0) and making an intercept of length 8 on the y-axis passes through the point :

A
(3,10)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(3,5)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(1,5)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(2,3)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (3,10)
Let r be the radius of the circle.
Equation of required circle is
(x3)2+(y±r)2=r2
x26x+9+y2±2ry+r2=r2
x2+y26x±2ry+9=0 (1)

Length of y-intercept of eqn. (1) is given by
2f2c ,f=±r
8=2r2916=r29r=5

So, required circle is
x2+y26x+10y+9=0 (2)x2+y26x10y+9=0 ...(3)
By putting all the points in these two equations, we get
(3,10) satisfies eqn. (3).

flag
Suggest Corrections
thumbs-up
100
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Intercepts Made by Circles on the Axes
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon