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Maths-

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Easy

Question

$left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 100$
In the xy-plane, the graph of the given equation is a circle. Which point (x , y) lies on the circle?

(3, -4)
(3, -1)
(3, 1)
(3, 4)

The correct answer is: (3, 4)

HINT :- upon observation from option substitute choose (3,a) such that it lies on the given circle $left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 100$ .And find the range of a and check the value that suits the range of from the options.
Explanation: upon observation from option substitute choose (3,a) such that it lies in the given circle $left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 100$
Step 1 : find range of a
For an point p, q to lie in circle $left parenthesis x minus a right parenthesis squared plus left parenthesis y minus b right parenthesis squared equals r squared$ then they should satisfy the given equation $left parenthesis p minus a right parenthesis squared plus left parenthesis q minus b right parenthesis squared minus r squared equals 0$
Step2 :Applying condition for the (3,a) then we get
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis 3 plus 3 right parenthesis squared plus left parenthesis a minus 7 right parenthesis squared minus 100 equals 0 end cell row cell 36 plus left parenthesis a minus 7 right parenthesis squared minus 100 equals 0 end cell row cell left parenthesis a minus 7 right parenthesis squared equals 64 text the end text a equals 7 minus 8 comma 7 plus 8 not stretchy rightwards double arrow a equals negative 1 comma 15 end cell end table$
So as per options a can be -1.
So (3,a) = (3,-1) lies on the given circle .

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