# Condition For Perpendicularity

## Trending Questions

**Q.**If the line x+y=1 touches the parabola y2−y+x=0, then the coordinates of the point of contact are

- (1, 1)
- (12, 12)
- (0, 1)
- (1, 0)

**Q.**If from a point P, 3 normals are drawn to parabola y2=4ax, then the locus of P such that one of the normal is angular bisector of other two normals is

- (2x−a)(x−5a)=27ay2
- (2x−a)(x+5a)=27ay2
- (2x−a)(x−5a)2=27ay2
- (2x−a)(x+5a)2=27ay2

**Q.**If a ray of light along the line y=4 gets reflected from a parabolic mirror whose equation is (y−2)2=4(x+1), then equation of reflected ray will be

- y=2
- x=2
- y=0
- x=0

**Q.**Equation of a tangent to the hyperbola 5x2−y2=5 and which passes through an external point (2, 8) is

- 3x−y+2=0
- 3x+y−14=0
- 23x−3y−22=0
- 3x−23y+178=0

**Q.**If at x=1, y=2x is tangent to the parabola y=ax2+bx+c, then which of the following option(s) is/are correct?

- a=c
- a, b, c are in A.P
- infinite such parabolas exist
- 2a+c=2

**Q.**If (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then its equation is

- x2+8y=32
- y2+8x=32
- y2−8x=32
- x2−8y=32

**Q.**

Which of the following statements are correct for oblique hyperbola xy = 8

1. Equation of tangent at P(4, 2) is x + 2y = 8

2. Equation of normal at P(t) is xt3 − yt = 2√2 (t4 − 1)

only 1

only 2

Both 1 & 2

None of these

**Q.**One end of a diameter of the circle x2+y2−6x+5y−7=0 is (-1, 3). Find the co-ordinates of the other end.

**Q.**The centre of a clock is taken as origin At 4.30 pm the equation of line along minute hand is x = 0 Therefore at this instant the equation of line along the hour hand will be

- x−y=0
- x+y=0
- y=√2x
- y=x√2

**Q.**If at x=1, y=2x is tangent to the parabola y=ax2+bx+c, then which of the following option(s) is/are correct?

- a=c
- a, b, c are in A.P
- infinite such parabolas exist
- 2a+c=2

**Q.**A ray of light travels along the line 2x−3y+5=0 and strikes a plane mirror lying along the line x+y=2. The equation of the straight line containing the reflected ray is

- 2x−3y+3=0
- 21x−7y+1=0
- 21x+7y−1=0
- 3x−2y+3=0

**Q.**The line y=−1 intersects the parabola y=x2−10x+24 at one point. Find the coordinates of the point of the intersection.

- (−5, −1)
- (24, −1)
- (0, −1)
- (5, −1)
- (35, −1)

**Q.**L1 & L2 are the two lines which passes through the point (1, −1) and tangent to the curve y=x2−3x+2. Then which of the following point(s) lie on the hyperbola having L1 & L2 as its asymptotes and passing through the origin?

- (2, −2)
- (−23, −2)
- (83, 0)
- (−2, −2)

**Q.**If a ray of light along the line y=4 gets reflected from a parabolic mirror whose equation is (y−2)2=4(x+1), then equation of reflected ray will be

- y=0
- x=0
- y=2
- x=2

**Q.**

If a source of light is placed at the focus of a parabola & if the parabola is a reflecting surface, then the ray reflected off the parabola bounces back in a line parallel to the axis of the parabola.

On the basis of above information answer the following question

- 3x+2y=16
- 4x+3y=16
- 5x+4y=9
- None of these

**Q.**A light beam emanating from the point A(3, 10) reflects from the line 2x+y−6=0 and then passes through the point B(5, 6). The equation of the incident and reflected beams respectively are:

- 4x−3y+18=0 and y=6
- x−2y+8=0 and x=5
- x+2y−8=0 and y=6
- None of these

**Q.**If one of the diameters of the circle x2+y2−2x−6y+6=0 is a chord to the circle with centre (2, 1), then the radius of the circle is:

- 3
- 2
- 32
- 1

**Q.**If the line x+y=1 touches the parabola y2−y+x=0, then the coordinates of the point of contact are

- (1, 1)
- (12, 12)
- (0, 1)
- (1, 0)

**Q.**If from a point P, 3 normals are drawn to parabola y2=4ax, then the locus of P such that one of the normal is angular bisector of other two normals is

- (2x−a)(x−5a)2=27ay2
- (2x−a)(x+5a)2=27ay2
- (2x−a)(x−5a)=27ay2
- (2x−a)(x+5a)=27ay2

**Q.**If a ray of light along the line y=4 gets reflected from a parabolic mirror whose equation is (y−2)2=4(x+1), then equation of reflected ray will be

- y=0
- x=0
- y=2
- x=2

**Q.**Assertion :A ray of light passes through (0, 0) after reflection at the point P(x, y) of any curve becomes parallel to x-axis, the equation of the curve may be a parabola y2=2x+1 Reason: A ray of light parallel to axis after reflection from parabolic mirror always passes through (0, 0)

- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- Assertion is correct but Reason is incorrect
- Both Assertion and Reason are incorrect

**Q.**The radius of the locus by the point represented by z, when argz−1z+1=π4, is

- √2π
- π√2
- none of these
- √2

**Q.**The area of the closed figure bounded by y=x, y=−x & the tangent to the curve y=√x2−5 at the point (3, 2) is

- 5
- 2√5
- 10
- 52

**Q.**A ray of light is coming along the line y=b from the positive direction of x− axis and strikes the concave mirror whose interaction with x− plane is a parabola y2=4ax. Find the equation of the reflected ray. Assume a, b are positive.

- (y−b)(4a2−b2)=(4ax+b2)
- (y+b)(4a2+b2)=−(4ax−b2)
- (y+b)(4a2−b2)=(4ax−b2)
- (y−b)(4a2−b2)=−(4ax−b2)

**Q.**ABC is a variable triangle such that A is (1, 2) and B and C on the line y=x+λ . Then the locus of the orthocenter of ΔABC is

- x+y=0
- x+y=3
- x−y=0
- x2+y2=4

**Q.**If the line x+y=1 touches the parabola y2−y+x=0, then the coordinates of the point of contact are

- (1, 1)
- (12, 12)
- (0, 1)
- (1, 0)