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  • Considered the graphs of  <img alt="\mathrm{y=A x^2 \text { and } y^2+3=x^2+4 y}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%3DA%20x%5E2%20%5Ctext%20%7B%20and%20%7

Considered the graphs of  \mathrm{y=A x^2 \text { and } y^2+3=x^2+4 y}, where A is

a positive constant and \mathrm{x, y \in R}. The number of points in which

the two graphs intersect is

Option: 1

4


Option: 2

3


Option: 3

5


Option: 4

None of these


Answers (1)

best_answer

We have  \mathrm{y=A x^2, y^2+3=x^2+4 y ; A>0}

Now,  \mathrm{y^2-4 y=x^2-3}

or, \mathrm{(y-2)^2=x^2+1}

or  \mathrm{(y-2)^2-x^2=1}

If X=0 , then

y-2=1 or -1

i.e.,  y=3 or 1

Hence, the two graphs of   \mathrm{y=A x^2(A>0)}  and the hyperbola

\mathrm{(y-2)^2-x^2=1}  are shown which intersects at four points.

Posted by

Rakesh

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