Parametric Equation of Normal
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Q.
The distance between the -axis and the point is:
Q. If a chord which is normal to the parabola y2=4ax at one end subtends a right angle at the vertex, then its slope can be
- √2
- −√2
- 2
- −2
Q. The chord x+y=1 of the curve y2=12x cuts it at the points A and B. The normals at A and B intersect at C. If a third line from C cuts the curve normally at D, then the co-ordinates of D are
- (3, −6)
- (12, −12)
- (6, −3)
- (12, 12)
Q.
Find the equation of normal to the parabola y2=8x at (8, 8) using parametric form.
2x + y = 24
2x - y = 24
x + y = 24
2x + y + 24 = 0
Q.
Find the equation of normal to the parabola y2=4ax at (at2, 2at) in terms of t, a.
y=tx+at3+2at
y=−tx+at3−2at
y=−tx+at3+2at
y=−tx+at3+at
Q. If a variable chord PQ of the parabola y2=4ax is drawn parallel to y=x, then the locus of point of intersection of normals at P and Q is
- 2x−y−12a=0
- 2x−y+10a=0
- 2x−y−8a=0
- 2x−y+6a=0
Q. Let P be the point on the parabola y2=4x, which is at the shortest distance from the centre S of the circle x2+y2−4x−16y+64=0. Let Q be the point on the circle dividing the line segment SP internally. Then,
- SP=2√5
- SQ:QP=(√5+1):2
- The x-intercept of the normal to the parabola at P is 6
- The slope of the tangent to the circle at Q is 12
Q. The locus of point P when three normals drawn from it to parabola y2=4ax are such that two of them make complementary angles is
- y2=a(x−a)
- y2=x−a
- x2=a(y−a)
- x2=y−a
Q. Let L be an end of the latus rectum of y2=4x. If the normal at L meets the curve again at M and the normal at M meets the curve again at N, then area of △LMN (in sq. units) is
- 12809
- 6409
- 3209
- 1609
Q. A normal is drawn to the parabola y2=9x at the point P(4, 6). A circle is described on SP as a diameter, where S is the focus. If the length of the intercept(in units) made by the circle on the normal at point P is L units, then the value of 8L is (units)
Q. The equation of the locus of the point of intersection of two normals to the parabola y2=4ax which are perpendicular to each other is
- y2=a(x−3a)
- y2=a(x+3a)
- y2=a(x+2a)
- y2=a(x−2a)