Bunuel wrote:

At how many points does the parabola y = 1/2*x^2 intersect the hyperbola x^2 – y^2 = 1?

A. 0

B. 1

C. 2

D. 3

E. 4

Second method to solve the question is to find the solutions algebraically

Given,

Parabola y = 1/2*x^2 i.e. x^2 = 2y

Hyperbola x^2 – y^2 = 1

Substitute the value of x^2 from equation of parabola to equation of Hyperbola

x^2 – y^2 = 1

i.e. (2y) – y^2 = 1

i.e. y^2 - 2y + 1 = 0

i.e. (y-1)^2 = 0

i.e. y = 1

Substituting the value of y to fin the value of x

x^2 = 2*1=2

i.e. x =

+\(\sqrt{2}\)

Hence, 2 points of Intersections

Answer: Option C

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