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Equation of the chord of the hyperbola 25x2 – 16y2 = 400 which is bisected at the point (6, 2) is
- a)16x – 75y = 418
- b)75x – 16y = 418
- c)25x – 4y = 400
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Equation of the chord of the hyperbola 25x2–16y2= 400 which is b...
Given hyperbola is 25x2−16y2=400
If (6, 2) is the midpoint of the chord, then equation of chord is T = S1
⇒25(6x)−16(2y)=25(36)−16(4)
⇒75x−16y=450−32
⇒75x−16y=418
If (6, 2) is the midpoint of the chord, then equation of chord is T = S1
⇒25(6x)−16(2y)=25(36)−16(4)
⇒75x−16y=450−32
⇒75x−16y=418
Most Upvoted Answer
Equation of the chord of the hyperbola 25x2–16y2= 400 which is b...
Given hyperbola is 25x2−16y2=400
If (6, 2) is the midpoint of the chord, then equation of chord is T = S1
⇒25(6x)−16(2y)=25(36)−16(4)
⇒75x−16y=450−32
⇒75x−16y=418
If (6, 2) is the midpoint of the chord, then equation of chord is T = S1
⇒25(6x)−16(2y)=25(36)−16(4)
⇒75x−16y=450−32
⇒75x−16y=418
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Equation of the chord of the hyperbola 25x2–16y2= 400 which is b...
Equation of the Chord of the Hyperbola:
Given Hyperbola Equation: 25x^2 - 16y^2 = 400
Bisected at the Point (6, 2):
The chord is bisected at the point (6, 2), which means the midpoint of the chord is (6, 2).
Midpoint Formula:
The midpoint formula for a line segment with endpoints (x1, y1) and (x2, y2) is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using Midpoint Formula:
Given point (6, 2) is the midpoint, we can find the other endpoint of the chord.
Equation of the Chord:
Once we have the two endpoints of the chord, we can find the equation of the chord using the two-point form of the equation of a line.
Options Analysis:
Now, we need to substitute the endpoints into the given options to see which equation satisfies the conditions.
Correct Answer: Option B) 75x - 16y = 418
Explanation:
By substituting the endpoints into option B, we can verify that this equation represents the chord that is bisected at the point (6, 2) for the given hyperbola.
Given Hyperbola Equation: 25x^2 - 16y^2 = 400
Bisected at the Point (6, 2):
The chord is bisected at the point (6, 2), which means the midpoint of the chord is (6, 2).
Midpoint Formula:
The midpoint formula for a line segment with endpoints (x1, y1) and (x2, y2) is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using Midpoint Formula:
Given point (6, 2) is the midpoint, we can find the other endpoint of the chord.
Equation of the Chord:
Once we have the two endpoints of the chord, we can find the equation of the chord using the two-point form of the equation of a line.
Options Analysis:
Now, we need to substitute the endpoints into the given options to see which equation satisfies the conditions.
Correct Answer: Option B) 75x - 16y = 418
Explanation:
By substituting the endpoints into option B, we can verify that this equation represents the chord that is bisected at the point (6, 2) for the given hyperbola.
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Equation of the chord of the hyperbola 25x2–16y2= 400 which is bisected at the point (6, 2) isa)16x –75y = 418b)75x –16y = 418c)25x –4y = 400d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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