If y1, y2, y3 be the ordinates of a vert...

If `y_1, y_2, y_3` be the ordinates of a vertices of the triangle inscribed in a parabola `y^2=4a x ,` then show that the area of the triangle is `1/(8a)|(y_1-y_2)(y_2-y_3)(y_3-y_1)|dot`

Topper's Solved these Questions

PARABOLA
ARIHANT MATHS|Exercise JEE type solved examples|1 Videos
PARABOLA
ARIHANT MATHS|Exercise Exercise For Session 1|20 Videos
PAIR OF STRAIGHT LINES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos
PERMUTATIONS AND COMBINATIONS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

If A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of the triangle then find area of triangle

Area of the equilateral triangle inscribed in circle x^2+y^2 -7x+ 9y+5 =0 is:

If the equations of three sides of a triangle are x+y=1, 3x + 5y = 2 and x - y = 0 then the orthocentre of the triangle lies on the line/lines

Show that the area of the triangle inscribed in the parabola y^2= 4ax is : (1)/(8a)|(y_(1)-y_(2))(y_(2)-y_(3))(y_(3)-y_(1))| , where y_(1),y_(2),y_(3) are the ordinates of the angular points.

Find the area of the equilateral triangle that can be inscribed in the circle : x^2 + y^2- 4x + 6y -3=0 .

Area of the triangle formed by the lines y=2x, y=3x and y=5 is equal to (in square units) :

Draw the graphs of the 5x-y=5 and 3x-y=3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2 equals

The equation of the sides of a triangle are x+2y+1=0, 2x+y+2=0 and px+qy+1=0 and area of triangle is Delta .

Show that the equation of the tangent to the parabola y^(2) = 4 ax at (x_(1), y_(1)) is y y_(1) = 2a(x + x_(1)) .

ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)

If y1, y2, y3 be the ordinates of a vertices of the triangle inscrib...
Text Solution
|
Let A and B be two finite sets such that n(A) =85, n(B) = 65and n(A ∪ ...
Text Solution
|
Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The l...
Text Solution
|
The axis of a parabola is along the line y=x and the distance of its v...
Text Solution
|
In a school, all pupils play either Hockey or Football or both. 400 pl...
Text Solution
|
The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...
Text Solution
|
The angle between the tangents to the curve y=x^2-5x+6 at the point (2...
Text Solution
|
Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...
Text Solution
|
Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...
Text Solution
|
Find slope of tangent to the curve if equation is x^2 + y^2 = 9
Text Solution
|
Statement 1 : The curve y=-(x^2)/2+x+1 is symmetric with respect to th...
Text Solution
|
The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+"...
Text Solution
|
Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0. Then,
Text Solution
|
If a parabola has the origin as its focus and the line x = 2 as the ...
Text Solution
|
In a school, there are 30 teachers who teach Mathematics or Physics. O...
Text Solution
|
Let A and B be two distinct points on the parabola y^2=4x. If the ax...
Text Solution
|
If two tangents drawn from a point P to the parabola y2 = 4x are at ri...
Text Solution
|
Of the 125 students in an elementary school, 89 students play checkers...
Text Solution
|
What is the 5th term of this sequence 9, 13, 17, ...?
Text Solution
|
In a group of 400 people, 250 can speak Punjabi and 200 can speak Engl...
Text Solution
|
If f (x) = a cos (bx + c) + d, then what is the range of f (x)?
Text Solution
|