Straight Lines
Get insights from 177 questions on Straight Lines, answered by students, alumni, and experts. You may also ask and answer any question you like about Straight Lines
- 177
Questions
- 0
Discussions
- 0
Active Users
- 0
Followers
Have a question about Straight Lines? Ask our experts
Keep it short & simple. Type complete word. Avoid abusive language.
The number of integral values of k for which the line, 3x+4y=k intersects the circle, x²+y²-2x-4y+4=0 at two distinct points is.
The number of integral values of k for which the line, 3x+4y=k intersects the circle, x²+y²-2x-4y+4=0 at two distinct points is.
Circle x²+y²-2x-4y+4=0
⇒ (x-1)²+ (y-2)²=1
Centre: (1,2) radius=1
line 3x+4y-k=0 intersects the circle at two distinct points.
⇒ distance of centre from the line < radius
⇒ |3×1+4×2-k|/√ (3²+4²) < 1
⇒ |11-k|<5
⇒ 6
Number of K is 9.
Upvote 
Let P(h,k) be a point on the curve y = x² + 7x + 2, nearest to the line, y = 3x - 3. Then the equation of the normal to the curve at P is
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
Let P(h,k) be a point on the curve y = x² + 7x + 2, nearest to the line, y = 3x - 3. Then the equation of the normal to the curve at P is
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
Let L be the common normal to parabola
y = x²+7x+2 and line y = 3x-3
⇒ slope of tangent of y=x²+7x+2 at P=3
⇒ dy/dx|for p = 3
⇒ 2x+7=3 ⇒ x=-2 ⇒ y=-8
So P (-2, -8)
Normal at P: x+3y+C=0
⇒ C=26 (satisfies the line)
Normal: x+3y+26=0
Upvote Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
Kindly go through the solution
(3!)³ (4!)
Upvote Let L₁ be a tangent to the parabola y²=4(x+1) and L₂ be a tangent to the parabola y²=8(x+2) such that L₁ and L₂ intersect at right angles. Then L₁ and L₂ meet on the straight line:
Let L₁ be a tangent to the parabola y²=4(x+1) and L₂ be a tangent to the parabola y²=8(x+2) such that L₁ and L₂ intersect at right angles. Then L₁ and L₂ meet on the straight line:
Equation of tangent to y²=4 (x+1) is y=m (x+1)+1/m.
Equation of tangent to y²=8 (x+2) is y=m' (x+2)+2/m'.
m'=-1/m.
Solving for intersection point, x+3=0.
Upvote The locus of the mid - points of the perpendiculars drawn from points on the line, to the line is:
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
The locus of the mid - points of the perpendiculars drawn from points on the line, to the line is:
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
Slope AB = (k-α)/(h-2α) = -1
⇒ α = (k+h)/3
also (β+2α)/2 = h, (β+α)/2 = k
α = 2h - 2k
From (1) and (2)
(h+k)/3 = 2h - 2k
⇒ 5h = 7k
⇒ 5x = 7y
Upvote If the length of the chord of the circle, x²+y²=r²(r>0) along the line y-2x=3 is r, the r² is equal to:
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
If the length of the chord of the circle, x²+y²=r²(r>0) along the line y-2x=3 is r, the r² is equal to:
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->
AB = r, AD = r/2
CD = rsin60° = √3r/2
|0+0-3|/√ (1²+2²) = √3r/2 ⇒ 3/√5 = √3r/2 ⇒ r = 2√3/√5 ⇒ r² = 12/5
Upvote