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14 Mar 2018, 00:00
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D
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Difficulty:
45%
(medium)
Question Stats:
61% (01:22) correct
39%
(01:43)
wrong
based on 69
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A circle passes through the point (5,0). What is the area of this circle?
(1) This circle also passes through points (3,4) and (-4,3).
(2) Centre of this circle is at (0,0).
(1) This circle also passes through points (3,4) and (-4,3).
(2) Centre of this circle is at (0,0).
14 Mar 2018, 13:57
Kudos
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A circle passes through the point (5,0). What is the area of this circle?
(1) This circle also passes through points (3,4) and (-4,3).
The general form of the circle is x^2 + y^2 + Dx + Ey + F = 0
(3,4): 3^(2)+4^(2) + 3D + 4E + F =0 -> 3D + 4E + F = -25 * 3 -> 9D + 12E + 3F = -75 -> (1)
(4,-3): 4^(2)+(-3)^(2) + 4D - 3E + F =0 -> 4D - 3E + F = -25 * 4 -> 12D - 12E + 4F = -100 -> (2)
(5,0): (5)^(2)+5D+F = 0 -> 5D + F = -25 -> (3)
Adding equations (1) and (2), we get 21D + 7F = - 175 -> 3D + F = -25 -> (4)
Solving equations (3) and (4), we get D = 0 and F = -25
Substituting these values in (2), we get E = 0.
We will get the equation of the circle \(x^2 + y^2 = (5)^2\)
The area of this circle is \(25*\pi\) (Sufficient)
(2) Centre of this circle is at (0,0).
If the circle's centre is (0,0) and it passes through the point (5,0)
The radius of the circle is the distance between these points, 5.
The area of this circle is \(25*\pi\) (Sufficient - Option D)
(1) This circle also passes through points (3,4) and (-4,3).
The general form of the circle is x^2 + y^2 + Dx + Ey + F = 0
(3,4): 3^(2)+4^(2) + 3D + 4E + F =0 -> 3D + 4E + F = -25 * 3 -> 9D + 12E + 3F = -75 -> (1)
(4,-3): 4^(2)+(-3)^(2) + 4D - 3E + F =0 -> 4D - 3E + F = -25 * 4 -> 12D - 12E + 4F = -100 -> (2)
(5,0): (5)^(2)+5D+F = 0 -> 5D + F = -25 -> (3)
Adding equations (1) and (2), we get 21D + 7F = - 175 -> 3D + F = -25 -> (4)
Solving equations (3) and (4), we get D = 0 and F = -25
Substituting these values in (2), we get E = 0.
We will get the equation of the circle \(x^2 + y^2 = (5)^2\)
The area of this circle is \(25*\pi\) (Sufficient)
(2) Centre of this circle is at (0,0).
If the circle's centre is (0,0) and it passes through the point (5,0)
The radius of the circle is the distance between these points, 5.
The area of this circle is \(25*\pi\) (Sufficient - Option D)
14 Mar 2018, 16:20
Kudos
Bookmarks
Given [5,0] lies on the circle.
(1) This circle also passes through points (3,4) and (-4,3).
let's say co-ordinate (x, y) denotes the centre of the circle .. distance from the centre to each of the given points will denote radius hence the distance will be same.
\((x -5)^2\)+ \(y^2\) = \((x -3)^2\)+ \((y-4)^2\) = \((x+4)^2\)+ \((y-3)^2\)
we know \(3^2\)+ \(4^2\) = 25 = \(5^2\)
so we make x = y = 0 in our equation : we get : 25 = 25 = 25 or 5 is the radius of the circle hence we can find the area.
(2) Centre of this circle is at (0,0). - radius = 5 hence we can find the area
ans : D
(1) This circle also passes through points (3,4) and (-4,3).
let's say co-ordinate (x, y) denotes the centre of the circle .. distance from the centre to each of the given points will denote radius hence the distance will be same.
\((x -5)^2\)+ \(y^2\) = \((x -3)^2\)+ \((y-4)^2\) = \((x+4)^2\)+ \((y-3)^2\)
we know \(3^2\)+ \(4^2\) = 25 = \(5^2\)
so we make x = y = 0 in our equation : we get : 25 = 25 = 25 or 5 is the radius of the circle hence we can find the area.
(2) Centre of this circle is at (0,0). - radius = 5 hence we can find the area
ans : D
