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A pair of tangent lines are drawn from the origin to the circle x2+y2+20(x+y)+20=0. The equation of pair of tangents is
- a)x2+y2+10xy=0
- b)x2+y2+5xy=0
- c)2x2+2y2+5xy=0
- d)x2+y2-5xy=0
Correct answer is option 'C'. Can you explain this answer?
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A pair of tangent lines are drawn from the origin to the circle x2+y2+...
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A pair of tangent lines are drawn from the origin to the circle x2+y2+...
Given information:
A pair of tangent lines are drawn from the origin to the circle x^2 + y^2 + 20x + 20y + 20 = 0.
To find:
The equation of the pair of tangents.
Solution:
To find the equation of the pair of tangents, we will follow these steps:
Step 1: Find the center of the circle
We have the equation of the circle as x^2 + y^2 + 20x + 20y + 20 = 0. To find the center, we need to complete the square.
Rearranging the terms, we have:
x^2 + 20x + y^2 + 20y = -20
Completing the square for x terms, we add (20/2)^2 = 100 to both sides:
x^2 + 20x + 100 + y^2 + 20y = -20 + 100
Simplifying the equation, we have:
(x + 10)^2 + (y + 10)^2 = 80
Comparing this equation with the standard form of a circle, we can see that the center of the circle is (-10, -10).
Step 2: Find the radius of the circle
The radius of the circle can be found by taking the square root of the constant term in the equation of the circle. In this case, the radius is √80.
Step 3: Find the equation of the tangents
The equation of a tangent line to a circle with center (a, b) and radius r can be written as:
(x - a)^2 + (y - b)^2 = r^2
Substituting the values from the given circle, we have:
(x + 10)^2 + (y + 10)^2 = 80
Expanding this equation, we get:
x^2 + 20x + 100 + y^2 + 20y + 100 = 80
Simplifying the equation, we have:
x^2 + y^2 + 20x + 20y + 120 = 80
Rearranging the terms, we get:
x^2 + y^2 + 20x + 20y + 40 = 0
So, the equation of the pair of tangents is x^2 + y^2 + 20x + 20y + 40 = 0, which is equivalent to option 'C'.
Therefore, the correct answer is option 'C'.
A pair of tangent lines are drawn from the origin to the circle x^2 + y^2 + 20x + 20y + 20 = 0.
To find:
The equation of the pair of tangents.
Solution:
To find the equation of the pair of tangents, we will follow these steps:
Step 1: Find the center of the circle
We have the equation of the circle as x^2 + y^2 + 20x + 20y + 20 = 0. To find the center, we need to complete the square.
Rearranging the terms, we have:
x^2 + 20x + y^2 + 20y = -20
Completing the square for x terms, we add (20/2)^2 = 100 to both sides:
x^2 + 20x + 100 + y^2 + 20y = -20 + 100
Simplifying the equation, we have:
(x + 10)^2 + (y + 10)^2 = 80
Comparing this equation with the standard form of a circle, we can see that the center of the circle is (-10, -10).
Step 2: Find the radius of the circle
The radius of the circle can be found by taking the square root of the constant term in the equation of the circle. In this case, the radius is √80.
Step 3: Find the equation of the tangents
The equation of a tangent line to a circle with center (a, b) and radius r can be written as:
(x - a)^2 + (y - b)^2 = r^2
Substituting the values from the given circle, we have:
(x + 10)^2 + (y + 10)^2 = 80
Expanding this equation, we get:
x^2 + 20x + 100 + y^2 + 20y + 100 = 80
Simplifying the equation, we have:
x^2 + y^2 + 20x + 20y + 120 = 80
Rearranging the terms, we get:
x^2 + y^2 + 20x + 20y + 40 = 0
So, the equation of the pair of tangents is x^2 + y^2 + 20x + 20y + 40 = 0, which is equivalent to option 'C'.
Therefore, the correct answer is option 'C'.
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A pair of tangent lines are drawn from the origin to the circle x2+y2+...
Bro use ss'=t^2 where t is tangnents from origin and s' is origin and get ur ans
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A pair of tangent lines are drawn from the origin to the circle x2+y2+20(x+y)+20=0. The equation of pair of tangents isa)x2+y2+10xy=0b)x2+y2+5xy=0c)2x2+2y2+5xy=0d)x2+y2-5xy=0Correct answer is option 'C'. Can you explain this answer?
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A pair of tangent lines are drawn from the origin to the circle x2+y2+20(x+y)+20=0. The equation of pair of tangents isa)x2+y2+10xy=0b)x2+y2+5xy=0c)2x2+2y2+5xy=0d)x2+y2-5xy=0Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A pair of tangent lines are drawn from the origin to the circle x2+y2+20(x+y)+20=0. The equation of pair of tangents isa)x2+y2+10xy=0b)x2+y2+5xy=0c)2x2+2y2+5xy=0d)x2+y2-5xy=0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pair of tangent lines are drawn from the origin to the circle x2+y2+20(x+y)+20=0. The equation of pair of tangents isa)x2+y2+10xy=0b)x2+y2+5xy=0c)2x2+2y2+5xy=0d)x2+y2-5xy=0Correct answer is option 'C'. Can you explain this answer?.
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