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Syllabus

Find the coordinates of foot of perpendicular from the point (2,3) to the line 3x+4y+8=0.

Find the locus of the point P such that the sum of it's distances from (0,2) and (0,-2) is 6.

Q.17 of miscellaneous ex. of N cert book chapter 10 st. line

The base of the equilateral triangle has an equation of x+2y=3 and one of the vertex is (1,1).find the equation of other two sides

the equation of the perpendicular bisectors of sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0respectively. if the point is A (1,-2), find the equation of line BC.

Two adjacent sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0.

If the equation of one of the diagonals is 11x + 7y = 4, find the equation

of the other diagonal.

A line is such that it's segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5) obtain it's equation?

if G is the centroid and I the incentre of the triangle with vertices A(-36,7) ,B(20,7) ,C(0,6) then find the value of GI?

sir, can u explain me how to find tan inverse in log books..

Find the equation of the bisector of the acute angle between the lines, 5x + 12y = 0 and 3x = 4y.

I tried solving this problem but a

_{1}a_{2}+ b_{1}b_{2}was equal to 0. Then in this case which equation would be taken as the equation of acute angle bisector between the two lines?find the coordinates of the incentre and centroid of the triangle whose sides have the equation 3x -4y=0, 12y+5x=0, y-15=0.

also please tell me what is incentre, circumcentre, orthocentre and centroid in a triangle

two sides of an isocesle triangle are given by the equation 7x-y+3=0 and x+y-3=0. if its third side passes through the point (1,-10) then its equations are-

anda1x + b1y + c1 = 0isa2x + b2y + c2 = 0(a1x + b1y + c1)=/(a1*alpha + b1*beta + c1)(a2x + b2y + c2)/(a2*alpha + b2*beta + c2)NO LINKS PLEASEThe hypotenuse of a right angled triangle has its ends at points

(1,3)and(-4,1).Find the equation of the legs (perpendicular sides) of the triangle.Thank You.

Find the image of the point (1,2) in the line x-3y+4 =0

Find K if (K,2 ) is an interior point of the triangle formed by the lines x+y=4, 3x-7y=8 and 4x-y=31.

Find the equations of the lines which pass through (4,5) and make equal angles with lines 5x-12y +6 =0 and 3x-4y-7=0

the distance of the point (3,5) from the line 2x +3y - 14 = 0 measured parallel to the line x - 2y = 1 is ?

a) 7/ root 5

b) 7/ root 13

c) root 5

d) root 13

NCERT - miscellaneous exercise ch 10 Q-17

The end points of the hypotenuse of a right angled triangle are (1,3) and (-4,1). Find the equation of the legs of the triangle.

if a^2 + b^2 - c^2 - 2ab = 0 , then family of st. lines ax+by+c=0 intersects at which point(s)?

Show that the points A(7,10), B(-2,5) and C(3,-4) are the vertices of an isoceles right-angled triangle.

A right angled triangle ABC having right angle at C, CA=b and CB=a, move such that the angular points A and B slide along x-axis and y-axis respectively. Find the locus of C.

The area of the triangle formed by the coordinate axes and a line is 6 square units and the length of the hypotenuse is 5 units . Find the equation of the line

find the equation of the line through the intersection of the lines 2x+3y-4 = 0 and x-5y = 7 that has its intercept equal to -4.

Find the equation of a line on which perpendicular from the origin makes an angle of 30 degree with the x-axis and which forma a triangle of area 50/3^1/2 with the coordinate axes ?

A ray of light passing through the point (1, 2) reflects on the

x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.$ax+by+c=0;ax+by+c\text{'}=0;a\text{'}x+b\text{'}y+c=0a\text{'}x+b\text{'}y+c\text{'}=0$ are at right angles. Also find the equation to the diagonals of the parallelogram.

P(3,1)Q(6,5)R(x,y) are 3 points such that the angle RPQ ia right angle then the area of triangle RPQ=7 then the no. Of such points R is.....

Ans. 2

1. find the equation of perpendicular bisectors of the line segment joining the points (1,1) and (2,3)

2. Find the eq of the line which passes through the points (3,4) and the sum of its intercepts on the axes 14

Find the orthocentre of the triangle the equation of whose sides are x+y=1, 2x+3y=6, 4x-y+4=0

if A(1,4) B(2,-3) C(-1,-2) are the vertices of a triangle ABC. find

a) the equation of the median through A

b) the equation of altitude through B

c) the right bisector of BC

The number of points P(x, y) lying inside or on the circle x

^{2}+y^{2}=9 and satisfying the equationtan

^{4}x+c0t^{4}x+2 =4 sin^{2}y is __ .One side of a rectangle lies along the line 4x + 7y + 5 = 0. Two of its

vertices are (–3, 1) and (1,1). Find the equation of other three sides.

Can you please derive the distance between two parallel lines' formula ??

A STRAIGHT LINE PASSES THROUIGH (2,3) AND THE PORTION OF HTE STRAIGHT LINE INTERCEPTED BETWEEEN THE AXES IS BISECTED AT THIS POINT.FIND ITS EQ.

if the image of the point(2,1) with respect to a line mirror be (5,2), find the equation of the mirror.

How to split a pair of line equation of ax

^{2}+2hxy+by^{2}+2gx+2fy+c=0 in the short method?Consider a family of straight lines (x + y) + lambda(2x - y + 1) = 0. Find the equation of the straight line belonging to this family that is farthest from (1, -3).

Kindly please don't refer me the link to a similar question that ha s already been answered as I tried that method but I got a wrong answer.

Thank You.

Find the eq. of the straight lines which go through the origin and trisect the portion of the straight line 3x+y=12 which is intetercepted between the axes of the coordinates.

^{2})^{1/2}+ t, 0] and B = [(1-t^{2})^{1/2}- t, 2t] are two variable points where t is a parameter, the locus of the middle point of AB isthe diagonal of a square lies along the line 8x-15y=0 one vertex is (1,2). find equations to the side of square passing through it?

This question is related to pairs of straight lines..

If the two pairs of lines x

^{2}− 2nxy − y^{2}= 0 and x^{2}− 2mxy − y^{2}= 0 are such that one of them representsthe bisector of the angles between the other, then mn + 1 is equal toFind the equation of bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)

Show that the points A(0,6), B(2,1) and C(7,3) are the three corners of a square ABCD. Find i) the slope of the diagonal BD and ii) the coordinates of the fourth vertex D.

Find the slope of the line, which makes an angle of 30° with the positive direction of

y-axis measured anticlockwise.what difference it will get when it become clockwise in place of aticlockwise.

the incenter of triangle formed by lines y=IxI y=1 is

find the equation of the straight line which cuts off intercepts on x axis twice that on y axis and is at a unit distance from the origin

a straight line makes an intercept on the y axis twice as long as that on the x axis and is at a unit distance from the origin.determine its equation (pls slove it)find the distance of the point (2,3) from the line 2x-3y+9=0 measured along a line making an angle of 45degreewith the x axis

(a)ac>0,bc>0

(b)ac>0 and bc<0

(c)bc>0 or ac>0

(d)ac<0 and / or bc<0

find what the following equation becomes when the origin is shifted to the point(1,1)

x

^{2}+xy-3y^{2}-y+2=0^{2}+1)x-y+q=0 and (p^{2}+1)^{2}x+(p^{2}+1)y+2q=0 are perpendicular to the common line for ?Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line

x–2y= 3.find the equation of passing through the point (3,2) and whose slope is 3/4. find the coordinates of the points on the same line that are 5 units away from the point (3,2)

the line 2x+3y=12 meets the x axis at A and y axis at B.The line through (5,5) perpendicular to AB meets the x axis and AB at C and.If O is the origin of coordinates ,find the area of OCEB

If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P.

the point P(a,b) lies on the straight line 3x+2y=13 and the point Q(b,a) lies on the straight line 4x-y=5, then the equation of line PQ is?

If

pandqare the lengths of perpendiculars from the origin to the linesxcosθ–ysinθ=kcos 2θandxsecθ+ycosecθ=k, respectively, prove thatp^{2}+ 4q^{2}=k^{2}Q. Example 77: Let A

_{0}_{ }A_{1}_{ }A_{2}_{ }A_{3}_{ }A_{4}_{ }A_{5}be a regular hexagon inscribed in a circle of unit radius then the product of the lengths of the line segments A_{0}A_{1}, A_{0}A_{2}and A_{0}A_{4}is(a) 3/4 (b) $3\sqrt{3}$

(c) 3 (d) $3\sqrt{3}$/ 2

Find the equation of the line through the intersection of lines 3x + 4y = 7 and x – y + 2 = 0 and

Reduce the equation 3x - 2y + 4 = 0 to the intercept form. Hence, find the length of the segment intercepted between the axes.

Find the equation of the circle passing through the points (1,2), (3,-4) and (5,-6)

if line joining A (2,0) AND B(3,1) is rotated abt A in anticlockwise direction thru an angle 15 . find equation of the line in new position