Monday, January 25, 2016

In how many points do the graphs of the equations x^2 + y^2 = 25 and y^2 = 4x intersect?

You need to remember that the coordinates of points that
lie on both curves need to be solutions of both
given equations.


You need to express `y^2`  in terms of
`x^2`  in the equation `x^2 + y^2 = 25 ` such that:


`y^2 =
25 - x^2`


You need to set the equations `y^2 = 25 - x^2` 
and `y^2 = 4x ` equal such that:


`25-x^2 =
4x`


`-x^2 - 4x + 25 = 0`


`x^2
+ 4x - 25 = 0`


You should complete the square such
that:


`x^2 + 4x + 4 - 4 - 25 =
0`


`(x+2)^2 - 29 = 0`


`(x+2)^2
= 29 =gt x+2 = +-sqrt29`


`x_1 = -2 +
sqrt29`


`x_2 = -2 -
sqrt29`


You need to find the coordinates `y_1`  and `y_2` 
such that:


`y_(1,2) =
+-sqrt(4(sqrt29-2))`


`y_(3,4) =
+-sqrt(4(-sqrt29-2))`


Hence, evaluating the
coordinates of points of intersection of curves yields `x_1 = -2 + sqrt29 ; y_(1,2) =
+-sqrt(4(sqrt29-2))`  and `x_2 = -2 - sqrt29 ; y_(3,4) = +-sqrt(4(-sqrt29-2)).`

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