Tangent and Normal of Parabola
Parabola

120248 If a normal chord at a point t(0) on the parabola y2=9x subtends a right angle at its vertex, then t=

1 3
2 5
3 ±3
4 ±2
Parabola

120250 If ax+by=1 is a normal to the parabola y2= 4px then the condition is

1 4ab=a2+b2
2 4pab+ab3=a2 b2
3 pa3=b22pab2
4 pa2+4pa=a+b
Parabola

120251 If P and the origin are the points of intersection of the parabolas y2=32x and 2x2=27y; and if θ is the acute angle between these curves at P, then 5tanθ=

1 2
2 23
3 32
4 3
Parabola

120252 The angle between the tangents drawn from the point (1,4) to the parabola y2=4x, is:

1 π/2
2 π/6
3 π/4
4 π/3
Parabola

120248 If a normal chord at a point t(0) on the parabola y2=9x subtends a right angle at its vertex, then t=

1 3
2 5
3 ±3
4 ±2
Parabola

120249 The locus of the points intersections of perpendicular normal's to the parabola y2= 4ax, is

1 y22ax+2a2=0
2 y2+ax+2a2=0
3 y2ax+2a2=0
4 y2ax+3a2=0
Parabola

120250 If ax+by=1 is a normal to the parabola y2= 4px then the condition is

1 4ab=a2+b2
2 4pab+ab3=a2 b2
3 pa3=b22pab2
4 pa2+4pa=a+b
Parabola

120251 If P and the origin are the points of intersection of the parabolas y2=32x and 2x2=27y; and if θ is the acute angle between these curves at P, then 5tanθ=

1 2
2 23
3 32
4 3
Parabola

120252 The angle between the tangents drawn from the point (1,4) to the parabola y2=4x, is:

1 π/2
2 π/6
3 π/4
4 π/3
Parabola

120248 If a normal chord at a point t(0) on the parabola y2=9x subtends a right angle at its vertex, then t=

1 3
2 5
3 ±3
4 ±2
Parabola

120249 The locus of the points intersections of perpendicular normal's to the parabola y2= 4ax, is

1 y22ax+2a2=0
2 y2+ax+2a2=0
3 y2ax+2a2=0
4 y2ax+3a2=0
Parabola

120250 If ax+by=1 is a normal to the parabola y2= 4px then the condition is

1 4ab=a2+b2
2 4pab+ab3=a2 b2
3 pa3=b22pab2
4 pa2+4pa=a+b
Parabola

120251 If P and the origin are the points of intersection of the parabolas y2=32x and 2x2=27y; and if θ is the acute angle between these curves at P, then 5tanθ=

1 2
2 23
3 32
4 3
Parabola

120252 The angle between the tangents drawn from the point (1,4) to the parabola y2=4x, is:

1 π/2
2 π/6
3 π/4
4 π/3
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Parabola

120248 If a normal chord at a point t(0) on the parabola y2=9x subtends a right angle at its vertex, then t=

1 3
2 5
3 ±3
4 ±2
Parabola

120249 The locus of the points intersections of perpendicular normal's to the parabola y2= 4ax, is

1 y22ax+2a2=0
2 y2+ax+2a2=0
3 y2ax+2a2=0
4 y2ax+3a2=0
Parabola

120250 If ax+by=1 is a normal to the parabola y2= 4px then the condition is

1 4ab=a2+b2
2 4pab+ab3=a2 b2
3 pa3=b22pab2
4 pa2+4pa=a+b
Parabola

120251 If P and the origin are the points of intersection of the parabolas y2=32x and 2x2=27y; and if θ is the acute angle between these curves at P, then 5tanθ=

1 2
2 23
3 32
4 3
Parabola

120252 The angle between the tangents drawn from the point (1,4) to the parabola y2=4x, is:

1 π/2
2 π/6
3 π/4
4 π/3
Parabola

120248 If a normal chord at a point t(0) on the parabola y2=9x subtends a right angle at its vertex, then t=

1 3
2 5
3 ±3
4 ±2
Parabola

120249 The locus of the points intersections of perpendicular normal's to the parabola y2= 4ax, is

1 y22ax+2a2=0
2 y2+ax+2a2=0
3 y2ax+2a2=0
4 y2ax+3a2=0
Parabola

120250 If ax+by=1 is a normal to the parabola y2= 4px then the condition is

1 4ab=a2+b2
2 4pab+ab3=a2 b2
3 pa3=b22pab2
4 pa2+4pa=a+b
Parabola

120251 If P and the origin are the points of intersection of the parabolas y2=32x and 2x2=27y; and if θ is the acute angle between these curves at P, then 5tanθ=

1 2
2 23
3 32
4 3
Parabola

120252 The angle between the tangents drawn from the point (1,4) to the parabola y2=4x, is:

1 π/2
2 π/6
3 π/4
4 π/3