Question

3/ Illustrate geometrically all solutions to the system of equations of a parabola and circle.

Answer 1

Solution:-

System of equations of circle and parabola can have 0 ,1 or 2 solutions.

For example-

0 solution:-

If equation of circle is x^{​​​​​2} + y^{​​​​​​2}​​​​​ = 1 and

equation of parabola is y = x^{​​​​​​2} + 2

Then there is no intersection point betweenbetween circle and parabola and hence there is no solution between them.

As shown in figure (1).

1 solution:-

If equation of circle is x^{​​​​​2} + y^{​​​​​​2}​​​​​ = 1 and

equation of parabola is y = x^{​​​​​​2} + 1

Then there is one intersection point between circle and parabola and hence there is only one solution between them.

As shown in figure (2).

2 solution:-

If equation of circle is x^{​​​​​2} + y^{​​​​​​2}​​​​​ = 1 and

equation of parabola is y = x^{​​​​​​2}

Then there are two intersection points between circle and parabola and hence there are 2 solutions between them.

As shown in figure (3).

y W Ч-и+2 2 Я и'+y'= | И о fig- st « =p+) M² + y2 = 1 — о - fig. 2 лу 2 9 - и е Н ер'+у? - А fig.]

Hence, there can be 0, 1 or 2 solutions between system of equations of circle and parabola.