Home
Class 12
MATHS
If the two circles 2x^2+2y^2-3x+6y+k=0 a...

If the two circles `2x^2+2y^2-3x+6y+k=0` and `x^2+y^2-4x+10 y+16=0` cut orthogonally, then find the value of `k` .

Text Solution

Verified by Experts

The given circles are
`2x^(2)+2y^(2)-3x+6y+k=0`
or `x^(2)+y^(2)-(3)/(2)x+3y+(k)/(2)=0` (1)
and `x^(2)+y^(2)-4x+10y+16=0` (2)
Since circles cut orthogonally, then
`2g_(1)g_(2)+2f_(1)f_(2)=c_(1)+c_(2)`
or `2(-(3)/(4))(-2)+2((3)/(2))5=(k)/(2)+16`
or `3+15=(k)/(2)+16` or `k=4`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE PUBLICATION|Exercise Examples|13 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 4.1|1 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

If the two circles 2x^(2) +2y^(2) -3x+6y+k=0 and x^(2) +y^(2) -4x +10y +16=0 cut orthogonally, then the vlaue of k is-

If the circles x^2 + y^2 + 2x + 2ky + 6 = 0 and x^2 + y^2 + 2ky + k = 0 intersect orthogonally, then k is equal to _____

If 4x^(2)+ py^(2) =45 and x^(2)-4y^(2) =5 cut orthogonally, then the value of p is

If x^2+y^2-4x-6y+13=0 , then find the value of (x+y):(y-x).

If the curves y^(2)= 4x and xy = k cut orthogonally, then the value of k^(2) will be-

The two circles x ^(2)+y^(2)-2x +22y +5=0 and x ^(2) + y^(2) +14 x+6y +k=0 intersect orthogonally provided k is equal to-

If the circles x^(2) + y^(2) + 2x + 2ky + 6 = 0 and x^(2) + y^(2) + 2ky + k = 0 intersect orthogonally , then k is equal to _

If the curves a y+x^2=7 and x^3=y cut orthogonally at (1,1) , then find the value adot

The circe x ^(2) +y^(2) +8y-4 =0 cuts the real circel x ^(2) +y^(2) +gx +4=0 orthogonally , then the value of g is-

A circle through the common points of the circles x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) - 2x - 6y + 1 = 0 has its centre on the line 4x - 7y - 19 = 0 . Find the centre and radius of the circle .