Home
Class 12
MATHS
If the equation (5x-1)^2+(5y-2)^2=(lambd...

If the equation `(5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2` represents an ellipse, then find values of `lambdadot`

Text Solution

Verified by Experts

Given equaiton is
`(x-(1)/(5))^(2)+(y-(2)/(5))^(2)=(lambda-1)^(2)[(3x+4y-1)/(sqrt(3^(2))+4^(2))]^(2)`
or `underset("Distance between p(x,y)" and S((1)/(5),(2)/(5)))ubrace(sqrt((x-(1)/(5))+(y-(2)/(5))^(2)))=underset(e)ubrace(lambda-1)underset(("distance of "P(x,y) "from line"3x+4y-1=0))ubrace((|3x+4y-1|)/(sqrt(3^(2)+4^(2)))`
Thus, we have
`SP=e*P M,` where `0ltelt1`
`:. o lt|lambda-1|lt1`
`rArr lambda epsi (0,2)- {1}`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the equation (10x-5)^(2)+(10y -4)^(2)=lambda^(2) (3x+4y-1)^(2) represents a hyperbola then

If the equation (x^(2))/( 3 - lambda) + (y^(2))/(lambda - 8) + 1 = 0 represents an ellipse, then (i) lambda lt 8 (ii) lambda gt 3 (iii) 3 lt lambda lt 8 (iv) lambda lt 3" or "lambda gt 8

If the equation x^(2)+y^(2)+6x-2y+(lambda^(2)+3lambda+12)=0 represent a circle. Then

Show that the equation (10x-5)^(2)+(10y-5)^(2)=(3x+4y-1)^(2) represents an ellipse, find the eccentricity of the ellipse.

If the equation 3x^2 + 3y^2 + 6lambdax + 2lambda = 0 represents a circle, then the value of lambda . lies in

The equation (x^2)/(2-lambda)+(y^2)/(lambda-5)+1=0 represents an elipse, if

Does equation (5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2) represents a parabola ?

Does equation (5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2) represents a parabola ?

if mu_21 is 1.5, then find the value of lambda_1/lambda_2.

If the equation (4 lambda - 3) x^(2) + lambda y ^(2) + 6x - 2y + 2 = 0 represents a circle, then its centre is