Find the equation of the circle whose centre is at the point (4, 5) and which touches the x-axis.
Find the co-ordinates of the points at which the circle cuts the y-axis.
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Step-by-step explanation:
equation of the circle with center at h and k is
(x - h)² + (y - k)² = r²
h = 4, k = 5 and r² = 4² + 5² => 16+25
=> 41
therefore equation of tbe circle is,
(x - 4)² + (y - 5)² = 41
=> x² + 16 - 8x + y² + 25 - 10y = 41
=> x² + y² - 8x - 10y + 41 - 41 = 0
=> x² + y² - 8x - 10y = 0
to find the point at which the circle cuts y axis,
put x = 0
=> 0² + y² - 8*0 - 10y = 0
=> y² - 10y = 0
=> y ( y - 10) = 0
=> y = 0 and y = 10
therefore the circle
touches y axis at y = 10
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