 ×     #### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```
Given the three circles x 2 +y 2 -16x+60=0, 3x 2 +3y 2 -36x+81=0,x 2 +y 2 -16x-12y+84=0,find (i)the point from which the tangents to them are equal in length and (ii)this length.

```
4 years ago Nishant Vora
IIT Patna
2467 Points
```							let that point be (h.k)Now we know that Length of tangent is given by root(S1)So length of tangent to circle 1 is root(h2+k2-16h+60)Similarily for other two and then equate all the lengths
```
4 years ago
```							Can you plz explain it clearly to me to understand?? thanking you Sir..............................................................................................................
```
4 years ago
```							The radical axis of two circles has the property that the tangents drawn from a point on it to both the circles will have the same length. Radical axis equation quite naturally is S1=S2 i.e. S1- S2 =0 which is a straight line.  So, for this problem, find the radical axes of any two pairs of circles and their intersection will give you the point you seek( in this problem though, the point is inside the circle and hence length of tangent is not meaningful)
```
4 years ago
```							S1: x^2+y^2-16x+60=0S2:3x^2+3y^2-36x+81=0 =>x^2+y^2-12x+27=0S3:x^2+y^2-16x-12y+84=0 S1-S2=0x^2+y^2-16x+60-x^2-y^2+12x-27=0-4x=-33x=33/4 S2-S3=0x^2+y^2-12x+27-x^2-y^2+16x+12y-84=04x+12y-57=0 S3-S1=0x^2+y^2-16x-12y+84-x^2-y^2+16x-60=0-12y+24=0-12y=-24y=24/12y=2 Therefore, (x,y)=(33/4,2)
```
2 years ago
```							FIRST SELECT ANY OF THE EQUATION OF THE CIRLE AND THEN PUT THE VALUE OF (x,y)=(33/4) root S1 =>root x^2+y^2-16x+60          =>root (33/4)^2+(2)^2-16(33/4)+60          =>root 1089/16+4-132+60          =>root 1089/16-68          =>root 1089-1088/16          =>root 1/16          =>1/4
```
2 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions