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Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0?
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Equations of the straight line which meets the circle x² y² =100 in tw...
Understanding the problem:
The given circle equation is x² + y² = 100, which is centered at the origin (0,0) with a radius of 10 units. We need to find the equations of the straight lines that intersect this circle at two points, each at a distance of 4 units from the point (8,6).
Approach:
1. Find the center of the circle.
2. Determine the points on the circle that are 4 units away from (8,6).
3. Use the point-slope form to find the equations of the straight lines passing through these points.
Calculations:
1. The center of the circle is at (0,0).
2. The points on the circle that are 4 units away from (8,6) are (8±3, 6±4) = (11,2) and (5,10).
3. Using the point-slope form, the equations of the lines passing through these points are:
- Line passing through (11,2): y - 2 = -3/4(x - 11) => 4x + 3y - 46 = 0
- Line passing through (5,10): y - 10 = 3/4(x - 5) => 4x - 3y - 50 = 0
Conclusion:
The equations of the straight lines that meet the circle x² + y² = 100 in two points, each point at a distance of 4 units from the point (8,6), are:
- 4x + 3y - 46 = 0
- 4x - 3y - 50 = 0
Therefore, the correct answer is option C) 4x + 3y - 46 = 0.
The given circle equation is x² + y² = 100, which is centered at the origin (0,0) with a radius of 10 units. We need to find the equations of the straight lines that intersect this circle at two points, each at a distance of 4 units from the point (8,6).
Approach:
1. Find the center of the circle.
2. Determine the points on the circle that are 4 units away from (8,6).
3. Use the point-slope form to find the equations of the straight lines passing through these points.
Calculations:
1. The center of the circle is at (0,0).
2. The points on the circle that are 4 units away from (8,6) are (8±3, 6±4) = (11,2) and (5,10).
3. Using the point-slope form, the equations of the lines passing through these points are:
- Line passing through (11,2): y - 2 = -3/4(x - 11) => 4x + 3y - 46 = 0
- Line passing through (5,10): y - 10 = 3/4(x - 5) => 4x - 3y - 50 = 0
Conclusion:
The equations of the straight lines that meet the circle x² + y² = 100 in two points, each point at a distance of 4 units from the point (8,6), are:
- 4x + 3y - 46 = 0
- 4x - 3y - 50 = 0
Therefore, the correct answer is option C) 4x + 3y - 46 = 0.
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Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0?
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Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0?.
Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Equations of the straight line which meets the circle x² y² =100 in two points each point at a distance of 4 unit from the point (8,6)?. A) 4x 3y-50 =0 B) 4x 3y-100=0 C) 4x 3y-46=0?.
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