Question

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is the point (1, 4).

Coordinates of Point A are (_____
,
_____)

Answer 1

Answer:

2,-3 point A

quadrant 2

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Answer 2

Answer:

Since the directrix is parallel to the x-axis, the parabola’s equation will be of the form y=ax2+bx+c . To obtain the equation from scratch (without memorising any forms), you need to know the definition of a parabola. A parabola is the locus of points that are equidistant from the focus and the directrix (eccentricity is 1). The distance from a point (x,y) on the parabola and the directrix is |y−5| . The distance from a point (x,y) on the parabola and the focus is (x−2)2+(y−3)2−−−−−−−−−−−−−−−√

Equating these two distances and squaring both sides gives (y−5)2=(x−2)2+(y−3)2 .

After expansion we get y2−10y+25=x2−4x+4+y2−6y+9

4y=−x2+4x+12

y=−14x2+x+3