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

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`

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Let S be the focus of y^2=4x and a point P be moving on the curve s...

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  2. If a!=0 and the line 2b x+3c y+4d=0 passes through the points of ...

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  3. If y1, y2, y3 be the ordinates of a vertices of the triangle inscr...

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  4. The circle x^2+y^2+2lambdax=0,lambda in R , touches the parabola y^2=...

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  5. If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...

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  6. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) , where c1a n dc2 are variable,...

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  7. A circle touches the x-axis and also thouches the circle with center ...

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  8. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

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  9. Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The l...

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  10. If the liney-sqrt(3)x + 3=0 cuts the parabola y^2=x + 2 at A and B, th...

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  11. The locus of a point on the variable parabola y^2=4a x , whose distan...

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  12. Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y...

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  13. The angle between the tangents drawn from the point (1,4) to the para...

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  14. Statement 1: There are no common tangents between the circle x^2+y^2...

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  15. If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then ...

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  16. C is the centre of the circle with centre (0,1) and radius unity. y=ax...

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  17. The set of points on the axis of the parabola (x-1)^2=8(y+2) from wher...

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  18. The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is...

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  19. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

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  20. The endpoints of two normal chords of a parabola are concyclic. Then ...

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