If (1, 1), (k, 2) are conjugate points with
respect to the circle
x² + y2 +8x +2y +3 = 0
then k=
- 12
- 1217
- 12/5
-4
Answers
Answer:
-1217
Step-by-step explanation:
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Given : (1, 1), (k, 2) are conjugate points with respect to the circle
x² + y2 +8x +2y +3 = 0
To Find : Value of k
Solution:
x² + y² + 8x + 2y + 3 = 0
=> (x + 4)² - 16 + ( y + 1)² - 1 + 3 = 0
=> (x + 4)² + ( y + 1)² = 14
x + 4 = X
y + 1 = Y
=> (X)² + ( Y)² = 14
x + 4 = X => 1 + 4 = X => X = 5
y + 1 = Y => 1 + 1 = Y => Y = 2
(1, 1) is (5 , 2)
(k , 2) is ( k + 4 , 3)
x₁ , y₁ and x₂ , y₂ are conjugate to circle x² + y² = r²
if x₁.x₂ + y₁.y₂ = r₂
=> 5 (k + 4) + 2(3) = 14
=> 5k + 20 + 6 = 14
=> 5k = -12
=> k = - 12/5
or Simply
(x + 4)² + ( y + 1)² = 14
=> (x + 4)(x + 4) + (y + 1)(y + 1) = 14
=> (1 + 4)(k + 4) + (1 + 1)(2 + 1) = 14
=> 5k + 20 + 6 = 14
=> k = -12/5
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