Maths-
General
Easy
Question
The graph in the xy-plane of the equation above is a circle. If the circle is translated downward a units such that the circle is tangent to the x-axis, the equation becomes
What is the value of a?
The correct answer is: 8
Step by step explanation:
Given:
Equation of circle: (x− 6)2 + (y − 3)2 = 25
Step 1:
Compare given equation with general equation of circle.
(x − 6)2 + (y − 3)2 = 25
(x − h)2 + (y − k)2 = r2
∴ h = 6, k = 3 and r = 5
⇒ center of circle is = (6, 3) and radius is 5 units.
Step 2:
The circle is represented on graph as shown below figure 1.
Step 2:
After translatating downwards by a units such that it is tangent to x-axis is shown in the above figure 2.
Step 3:
As it be clearly seen that, in order to make circle as tangent to x-axis, we have to translate the circle 8 units downward.
∵ EA + AD
5 units + 3 units
= 8 units
Step 4:
Now put a = 8 in (x − 6)2 + (y − 3 + a)2 = 25
We will get,
(x − 6)2 + (y − 3 + 8)2 = 25
(x − 6)2 + (y + 5)2 = 25
So, the new circle will be with center (6, - 5) and radius 5.
Hence, the value of a is 8.
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