    Question

# Find the ratio of the length of the tangents from any point on the circle 15x2+15y2−48x+64y=0 to the two circles 5x2+5y2−24x+32y+75=0, 5x2+5y2−48x+64y+300=0.

A
1:2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2:5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1:3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1:4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A 1:2Let P(h,k) be a point on the circle 15x2+15y2−48x+64y=0. ∴h2+k2−4815h+6415k=0⇒3(h2+k2)=(485h−645k) ⋯(1) Now let the tangent lengths be PT1 and PT2 from P(h,k) to 5x2+5y2−24x+32y+75=0 and 5x2+5y2−48x+64y+300=0, respectively. Then PT1=√h2+k2−245h+325k+15=√15−12(h2+k2) [ From (1)] and PT2=√h2+k2−485h+645k+60=√60−2(h2+k2) [ From (1)]=2√15−12(h2+k2) ∴PT1:PT2=1:2  Suggest Corrections  0      Similar questions
Join BYJU'S Learning Program
Select...  Related Videos   Tangent to a Circle
MATHEMATICS
Watch in App  Explore more
Join BYJU'S Learning Program
Select...