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505-555 (Easy)|   Geometry|      
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Bunuel
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What is the area of a circle if its center is at (3, O) and the circle 03 Nov 2020, 01:15
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80% (00:53) correct 20% (01:06) wrong based on 99 sessions

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What is the area of a circle if its center is at (3, 0) and the circle passes through (-1, -3)?

A. \(9\pi\)
B. \(10\pi\)
C. \(16\pi\)
D. \(25\pi\)
E. \(36\pi\)


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D
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What is the area of a circle if its center is at (3, O) and the circle 03 Nov 2020, 02:38
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Explanation:
x1=3, y1= 0, x2=-1, y2=-3
Radius will be : =√{(x2-x1)²+(y2-y1)²}
=√{(4)² + (3)²}
=√25
r=5

Area of circle = πr^2 = 25π

IMO-D
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What is the area of a circle if its center is at (3, O) and the circle 03 Nov 2020, 05:01
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Radius of the circle = sqrt((3-(-1))^2 + (0-(-3))^2)) = 5 (Distance between points (3,0) and (-1, -3) )

Area = π*r^2 = 25π

D
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What is the area of a circle if its center is at (3, O) and the circle 03 Nov 2020, 09:22
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The distance formula is an important and well used formula. While using this we need to be careful with negative numbers. There is another method, wherein you draw the diagram as shown below.

You will get a right angled triangle and we need to find the length of the hypotenuse, using Pythagoras's theorem.

Length AB = 4 units and BC = 3 units

Here we have a Pythagorean triplet and therefore the length of the hypotenuse = radius of the circle = 5 .


The Area = \(\pi * r^2 = 25\pi\)


Option D

Arun Kumar
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What is the area of a circle if its center is at (3, O) and the circle 03 Nov 2020, 10:15
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Using the distance formula, we know that: Distance = sqrt((3-(-1))^2 + (0-(-3))^2))
Coordinates : (3, 0) and (-1, -3)
Distance = 5

Area of circle= pi*r*r
Pi*25

IMO D
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What is the area of a circle if its center is at (3, O) and the circle 03 Nov 2020, 18:21
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Radius of circle = Distance between Centre (3, 0) and (-1, -3) = sqrt (4^2 + 3^2) = 5

Area of circle = Pi * (Radius^2)= 25*Pi

Answer is D
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What is the area of a circle if its center is at (3, O) and the circle 03 Nov 2020, 22:33
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Radius = √[(x2-x1)^2+(y2-y1)^2]
Here, x1=3, y1= 0, x2=-1, and y2=-3
r=√[4^2+3^2]
r=√25
r=5

Area of circle = πr^2 = 25π

Option D

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What is the area of a circle if its center is at (3, O) and the circle 06 Nov 2020, 00:37
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Bunuel
What is the area of a circle if its center is at (3, 0) and the circle passes through (-1, -3)?

A. \(9\pi\)
B. \(10\pi\)
C. \(16\pi\)
D. \(25\pi\)
E. \(36\pi\)


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Alternate way:

Eqn. of a circle
\((x-p)^2 -(y-q)^2=r^2\)

Where \(p\) and \(q\) are the coordinates of the center and \((x,y)\) are the points through which circle passes and \(r\) is the radius of the circle.
\((-1-3)^2 +(-3-0)^2= r^2\)
\(16+9=r^2\) so \(r^2=25\) hence \( r=5 \) and area of circle is \(25\pi\)
Ans-D

Hope it helps.
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