Question

the point diametrically opposite to the points p,q on a circle x2 +y2+2x+4y-3=0 is​

Answer 1

given the equation of circle

${x}^{2} + {y}^{2} + 2x + 4y - 3 = 0$

the center of the circle is (-1,-2)

in a circle centre is the midpoint of two ends of diameter

here given (p,q) is one end let the other end be(x,y)

=>>((p+x)/2,(q+y)/2)=(-1,-2)

=>> p+x=-2 & q+y=-4

=>> x=-2-p & y=-4-q

the point diametrically opposite to the points p,q on a circle x2 +y2+2x+4y-3=0 is (-2-p,-4-q)

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Answer 2

Answer:

LA be the required point with coordinate (x,y).

Given equation of circle:-

x

2

+y

2

+2x+4y−3=0

To find:- Coordinate of point A

Now,

x

2

+y

2

+2x+4y−3=0

(x+1)

2

+(y+2)

2

−2−4−3=0

(x+1)

2

+(y+2)

2

=(3)

2

From the above equation, the centre of the circle is (−1,−2).

Since AP is the diameter of the circle, the centre will be the mid-point of AB.

now, as centre is the mid-point of AB.

x-coordinate of centre =

2

x+1

​

y-coordinate of centre =

2

y+0

​

=

2

y

​

But the centre of circle is (−1,−2).

Therefore,

2

x+1

​

=−1⇒x=−3

2

y

​

=−2⇒y=−4

Thus the coordinate of A is (−3,−4).

Hence the correct answer is (B)(−3,−4).

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