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

Question 14
If the centre of a circle is (2a, a-7), then find the values of a , if the circle passes through the point (11,-9) and has diameter 102 units.

Open in App
Solution

By given condition,

Distance between the centre C(2a , a-7) and the point P(11,-9), which lie on the circle = Radius of circle
Radius of circle=(112a)2+(9a+7)2 ...(i)[distance between the points(x1,y1) and (x2,y2)d=(x2x1)2+(x2y1)2]Given that, length of diameter =102Length of radius =Length of diameter2=10222=52Put this value in Eq.(i), we get50=(112a)2+(2+a)250=121+4a244a+4+a2+4a5a240a+75=0a28a+15=0a25a3a+15=0 [by splitting the middle term]a(a5)3(a5)=0(a5)(a3)=0a=3,5Hence, the required values of a are 5 and 3.

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Distance Fomula
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon