IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

sagar90

1)equation of common tangent to parabola y^2 = 4x and x^2 = 32y is ??

2) wht is orthocentre??

3)also tell me how to solve sums in which we have to find locus?

for first one do anyone knw shortcut?

ashish_banga

EQUATION OF ANY TANGENT TO PARABOLA IS GIVEN BY
y = mx + a/m
EQUATION OF ANY TANGENT TO ABOVE PARABOLA IS GIVEN BY
y = mx + 1/m............................1
now this is also a tangent to second parabola. so it should satisfy it
put the value of y from 1 in the equation of second
it will be quadratic in x
then put D = 0
this will give the value of m

RATE ME

ashish_banga

orthocentre is the point of intersection of the altitudes drawn to the side of the triangle

studyid

yes ...... ashish is right ............

and u shud get the equation of the tangent which is common to both the parabola y^2=4ax and x^2=4by .................

as :

(a)^1/3 x + (b)^1/3 y + (ab)^2/3 = 0 ...........

and the value of the slope will b m = -(a/b)^1/3 ........

sagar90

guys also tell me if we r asked to find eqn of common tsngent to a ellipse and circle thn wht to do?

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