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Bunuel
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

Parabola y = 1/2*x^2

Hyperbola x^2 – y^2 = 1

The best method is to draw the figure...

The figure shows that total points of intersections are two in number

Answer: Option C
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nailin16
Are you sure such questions can come I forgot what does a parabola or hyperbole look like

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Hi @nalin16,

You are right about your apprehension. Parabola has been witnessed in GMAT however no incidence of Hyperbola has been witnessed so far so I also feel that that hyperbola can not be part of any question of GMAT yet.
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nailin16
Are you sure such questions can come I forgot what does a parabola or hyperbole look like

Sent from my SM-G600FY using GMAT Club Forum mobile app

Hi @nalin16,

You are right about your apprehension. Parabola has been witnessed in GMAT however no incidence of Hyperbola has been witnessed so far so I also feel that that hyperbola can not be part of any question of GMAT yet.

Yes, that's true, but consider: Do you really need to know anything about *either* parabolas or hyperbolas or what they look like to solve this problem?

See, for instance, your own second solution.
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AnthonyRitz
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nailin16
Are you sure such questions can come I forgot what does a parabola or hyperbole look like

Sent from my SM-G600FY using GMAT Club Forum mobile app

Hi @nalin16,

You are right about your apprehension. Parabola has been witnessed in GMAT however no incidence of Hyperbola has been witnessed so far so I also feel that that hyperbola can not be part of any question of GMAT yet.

Yes, that's true, but consider: Do you really need to know anything about *either* parabolas or hyperbolas or what they look like to solve this problem?

See, for instance, your own second solution.

No, you don't necessarily need to know what a parabola or hyperbola looks like- you just need to know how to effectively substitute the parabola in the hyperbola so as to derive points of intersection. Simple, intersection of hyperbola and parabola= substitute parabola into hyperbola. Now, you can also substitute for the x values- the GMAT just makes a bit more difficult to figure out which is faster and more effective to substitute.
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Bunuel
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
having serious issues with alzebra can u please help ?
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