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The equation of chord of the circle x2 + y2 = 8x bisected at the point (4, 3) is
- a)x = 3
- b)y = 3
- c)x = –3
- d)y = –3
Correct answer is option 'B'. Can you explain this answer?
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The equation of chord of the circle x2 + y2 = 8x bisected at the point...
T = S1 ⇒ x(4) + y(3) – 4 (x + 4) = 16 + 9 – 32
⇒ 3y – 9 = 0 ⇒ y = 3
⇒ 3y – 9 = 0 ⇒ y = 3
Most Upvoted Answer
The equation of chord of the circle x2 + y2 = 8x bisected at the point...
The given circle can be rewritten as (x-4)^2 + y^2 = 16. Let the endpoints of the chord be (x1, y1) and (x2, y2). Then, we have:
(x1-4)^2 + y1^2 = 16
(x2-4)^2 + y2^2 = 16
The midpoint of the chord is (4,3), so we have:
(x1+x2)/2 = 4
(y1+y2)/2 = 3
Solving for x1 and x2 in terms of y1 and y2, we get:
x1 = 8 - 2y1
x2 = 8 - 2y2
Substituting these into the equation for the circle, we get:
(8-2y1-4)^2 + y1^2 = 16
(8-2y2-4)^2 + y2^2 = 16
Simplifying and combining like terms, we get:
y1^2 - 4y1 + 3 = 0
y2^2 - 4y2 + 3 = 0
These are two quadratic equations that have roots of y1=1 and y1=3, and y2=1 and y2=3, respectively. This means that the chord passes through the points (6,1) and (2,3) or the points (2,1) and (6,3).
We can find the equation of the first chord using the point-slope form:
(y-1) = (3-1)/(6-2) * (x-6)
y = -x/2 + 4
And we can find the equation of the second chord using the same method:
(y-1) = (3-1)/(6-2) * (x-2)
y = x/2
Neither of these equations match any of the answer choices given, so the answer is none of the above.
(x1-4)^2 + y1^2 = 16
(x2-4)^2 + y2^2 = 16
The midpoint of the chord is (4,3), so we have:
(x1+x2)/2 = 4
(y1+y2)/2 = 3
Solving for x1 and x2 in terms of y1 and y2, we get:
x1 = 8 - 2y1
x2 = 8 - 2y2
Substituting these into the equation for the circle, we get:
(8-2y1-4)^2 + y1^2 = 16
(8-2y2-4)^2 + y2^2 = 16
Simplifying and combining like terms, we get:
y1^2 - 4y1 + 3 = 0
y2^2 - 4y2 + 3 = 0
These are two quadratic equations that have roots of y1=1 and y1=3, and y2=1 and y2=3, respectively. This means that the chord passes through the points (6,1) and (2,3) or the points (2,1) and (6,3).
We can find the equation of the first chord using the point-slope form:
(y-1) = (3-1)/(6-2) * (x-6)
y = -x/2 + 4
And we can find the equation of the second chord using the same method:
(y-1) = (3-1)/(6-2) * (x-2)
y = x/2
Neither of these equations match any of the answer choices given, so the answer is none of the above.
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The equation of chord of the circle x2 + y2 = 8x bisected at the point (4, 3) isa)x = 3b)y = 3c)x = –3d)y = –3Correct answer is option 'B'. Can you explain this answer?
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