Grade Upto college levelAnalytical Geometry

the normal to the curve at P(x,y) meets the x axis at G. If the distance of G from the origin is twice the abscissa of P , then the curve is a) ellipse b) parabola c) ellipse or hyperbola

vansh kharbanda

12 Years agoGrade Upto college level

4 Answers

Ajay Verma

12 Years ago

solution:

for any curve the equation of normal at ( X1, Y1)

(y- y1) = -1/m (x- X1) {where m = slope of tengent or say dy/dx at (x1, Y1) }

normal meets the X axis at G..

( 0 - y1) = -1/m (x- X1)

so x = m*Y1 + X1

so coordinates of G( m*Y1 + X1 , 0)

now ...distance of G from the origin is twice the abscissa of P

2X1 = m*Y1 + X1

X1 = m*Y1

m = X1/Y1

dy/dx (at X1, Y1) = X1/Y1

dy/dx = x/y

ydy = x dx

integrate both sides

y²/2 = x²/2 + c

x²/2 - y²/2 = c

so hyperbola..

Thanks and Regards,

Ajay verma,

askIITians faculty,

IIT HYDERABAD

vansh kharbanda

12 Years ago

thank you

vansh kharbanda

12 Years ago

but sir the answer says it can be both ellipse as well as hyperbola, so can u please prove this as an ellipse too.

Ayushi Agarwal

9 Years ago

The equation is |x1 + my1|=2|x1|So there are 2 equations possible one with positive and the other with negative

The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

View all Questions

the normal to the curve at P(x,y) meets the x axis at G. If the distance of G from the origin is twice the abscissa of P , then the curve is a) ellipse b) parabola c) ellipse or hyperbola

vansh kharbanda

4 Answers

Ajay Verma

vansh kharbanda

vansh kharbanda

Ayushi Agarwal

Other Related Questions on analytical geometry

The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)

show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0

A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.

Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d