3rd question please 3 The nearest point on the circle x2+y2-6x+4y-12=0 from (-5,4) is 1)(1,1) - Maths - Conic Sections

Question

3rd question please
3 The nearest point on the circle
x2+y2-6x+4y-12=0 from (-5,4) is
1)(1,1) 2)(-1,1)
3)(-1,2) 4)(-2,2)

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

We havex2+y2-6x+4y-12=0
iCentre is Q3,-2P-5,4Shortest or longest distance is always found along normal and nomralof circle  passes through centre
Hence nearest point will be found along line PQ whose equation isy+2=4+2-5-3x-3⇒y+2=6-8x-3⇒y+2=-34x-3⇒y=-34x+94-2⇒y=-34x+14=-3x+14
iiSolve i and iix2+-3x+142-6x+4-3x+14-12=0Solving the above quadratic equation we getx=-1 and x=7y=-3x+14When x=-1y=3+14=1Hence -1,1When x=7y=-21+14=-5Hence 7,-5By distance formula you can easily see that -5,4 is nearer to -1,1Hence option2 is correct
Note: 7,-5 is farthest from -5,4

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3rd question please 3. The nearest point on the circle x2+y2-6x+4y-12=0 from (-5,4) is 1)(1,1) 2)(-1,1) 3)(-1,2) 4)(-2,2)

3rd question please
3. The nearest point on the circle x²+y²-6x+4y-12=0 from (-5,4) is
1)(1,1) 2)(-1,1)
3)(-1,2) 4)(-2,2)