If a focal chord of y^2=4a x makes an an...

If a focal chord of `y^2=4a x` makes an angle `alpha in [0,pi/4]` with the positive direction of the x-axis, then find the minimum length of this focal chord.

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
CENGAGE ENGLISH|Exercise All Questions|886 Videos
DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS
CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If a focal chord of y^(2)=4ax makes an angle alphain[pi//4,pi//2] with the positive direction of the x-axis, then find the maximum length of this focal shord.

A circle of radius 5 units has diameter along the angle bisector of the lines x+y=2 and x-y=2. If the chord of contact from the origin makes an angle of 45^0 with the positive direction of the x-axis, find the equation of the circle.

If a line makes an angle of pi/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of z-axis is

If a line makes an angle of pi/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is (1) pi/6 (2) pi/3 (3) pi/4 (4) pi/2

If a line makes an angle of pi/4 with the positive direction of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is a. pi/3 b. pi/4 c. pi/2 d. pi/6

If a line makes an angle of pi/4 with the positive direction of each of x-axis and y-axis, then the angel that the line makes with the positive direction of the z-axis is a. pi/3 b. pi/4 c. pi/2 d. pi/6

Show that the focal chord, of parabola y^2 = 4ax , that makes an angle alpha with the x-axis is of length 4a cosec^2 alpha .

If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

The length of a focal chord of the parabola y^2=4ax making an angle theta with the axis of the parabola is (a> 0) is :

A line (2,3) makes an angle (3pi)/4 with the negative direction of X- axis . Find the length of the line segment cut off between (2,3) and the line x+y - 7 = 0

CENGAGE ENGLISH-CONIC SECTIONS-All Questions

Find the number of distinct normals that can be drawn from (-2,1) to t...
Text Solution
|
If the line passing through the focus S of the parabola y=a x^2+b x+c ...
Text Solution
|
If a focal chord of y^2=4a x makes an angle alpha in [0,pi/4] with the...
Text Solution
|
Find the length of the normal chord which subtends an angle of 90^@ at...
Text Solution
|
Find the locus of the point of intersection of the normals at the end ...
Text Solution
|
The abscissa and ordinates of the endpoints Aa n dB of a focal chord o...
Text Solution
|
If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l1, t...
Text Solution
|
A circle is drawn to pass through the extremities of the latus rectum ...
Text Solution
|
Circles drawn on the diameter as focal distance of any point lying on...
Text Solution
|
If the length of a focal chord of the parabola y^2=4a x at a distance ...
Text Solution
|
Find the equation of the parabola whose focus is S(-1,1) and directrix...
Text Solution
|
If x^2 + y^2 = log(xy) , find dy/dx .
Text Solution
|
If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , the...
Text Solution
|
Prove that the length of the intercept on the normal at the point P(a ...
Text Solution
|
Find the minimum distance between the curves y^2=4x and x^2+y^2-12 x+3...
Text Solution
|
If y=2x+3 is a tangent to the parabola y^2=24 x , then find its distan...
Text Solution
|
Three normals to y^2=4x pass through the point (15, 12). Show that one...
Text Solution
|
Find the locus of the point from which the two tangents drawn to the ...
Text Solution
|
Find the angle between the tangents drawn from the origin to the parab...
Text Solution
|
Find the locus of the point of intersection of the perpendicular ta...
Text Solution
|