The line 5x-y=3 is tangent to …
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Gaurav Seth 6 years, 11 months ago
The equation is:
(x−7)2+(y−−6)2=(√26)2
Explanation:
Write the equation of the tangent line in slope-intercept form so that we may observe its slope.
y=−5x+3
The slope m=−5
Because radius of the circle at point (2, -7) will be perpendicular to the tangent line, the slope of the radius is the negative reciprocal of the slope of the tangent line, 15, Write the equation of the line through the point with this slope:
−7=15(2)+b
b=−7−25
b=−375
y=15x−375 [1]
The center (h,k) will be at the intersection of equation [1] and the line:
x−2y=19 [2]
Substitute equation [1] into equation [2]:
x−2(15x−375)=19
x−25x+745=19
35x=215
x=7
Substituting for x in equation [2]:
7−2y=19
−2y=12
y=−6
Substitute the center (7,−6) and the point (2,−7) into the equation of a circle:
(2−7)2+(−7−−6)2=r2
#r = sqrt(26)
5Thank You