Question

# Equation of the line passing through the mid-point of intercepts made by the circle x2 + y2 − 17x − 16y + 60 = 0 is

A

17x 16y = 136

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

16x + 17y = 136

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

17x + 16y = 136

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

16x 17y = 136

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C 16x + 17y = 136 Method 1: we will first find the points where the given circle intersect the coordinate axes .To find those points ,we will put y=0 and x=0 seperately. To find the x-coordinate x2 + y2 − 17x − 16y + 60 = 0 is the equation of given circle. when the circle intersects the x-axis ,y-coordinate will be zero. ⇒ x2 − 17x + 60 = 0 ⇒ (x−12)(x−5) = 0 ⇒ x=5 or x=12 so the points where it intersects x-axis are (5,0) and (12,0) ⇒ The mid-point ≡ (12+52,0) =(172,0) To find the y-coordinate when the circle intersects the y -axis ,the x-coordinate will be zero. ⇒ y2 − 16y + 60 = 0 ⇒ (y−10)(y−6)=0 ⇒ y=10 or y=6 so the points are (0,10) and (0,6) and the mid-point is (0,10+62) ≡ (0,8) we found that the mid-points are (172,0) and (0,8).we will now find the equation of the straight line passing these points ⇒ x172 + y8 = 1 or 2x17 + y8 = 1 ⇒ 16x + 17y = 136

Suggest Corrections
0
Related Videos
Basics Revisted
MATHEMATICS
Watch in App