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Syllabus

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

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

~~The sides of a triangle are given by the equation 3x+4y=10,4x-3y=5, and 7x+y+10=0. Show that the origin lies within the triangle.

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

(A) ${x}^{2}+{y}^{2}-5x+7y=0$ (B) ${x}^{2}+{y}^{2}+5x-7y=0$

(B) ${x}^{2}+{y}^{2}+5x+7y=0$ (C) ${x}^{2}+{y}^{2}-5x-7y=0$

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?

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

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

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

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-

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

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

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.

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

The point P is (2,3)

Find

1) If P is the centroid, then find p+q

2) If P is the orthocentre, the find p+q

3) If P is the circumcentre, then find p+q.

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.

derive the formula for the angle between the two straight lines y=m1x+c1 and y=m2x+c2 and hence find the angle between the lines y-root3-5=0 and root3y-x+6=0

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

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.

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.Find the equation of the line through the intersection of 5x-3y-1=0 and 2x+3y-23=0 and

a)perpendicular to line whose equation is 5x-3y-1=0

b) parallel to the line 4x+5y-7=0

Q2. If (a cos ${\mathrm{\theta}}_{1},\mathrm{a}\mathrm{sin}{\mathrm{\theta}}_{2}$), (a cos $\mathrm{\theta}$

_{2}, a sin $\mathrm{\theta}$_{2}) and (a cos $\mathrm{\theta}$_{3}, a sin $\mathrm{\theta}$_{3}) represents the vertices of an equilateral triangle inscribed inscribed in a circle, then(A) cos$\mathrm{\theta}$

_{1}+ cos$\mathrm{\theta}$_{2}+ cos$\mathrm{\theta}$_{3}= 0 (B) sin $\mathrm{\theta}$_{1}+ sin $\mathrm{\theta}$_{2}+ sin $\mathrm{\theta}$_{3}= 0(C) tan$\mathrm{\theta}$

_{1}+ tan$\mathrm{\theta}$_{2}+ tan$\mathrm{\theta}$_{3 }= 0 (D) cot$\mathrm{\theta}$_{1}+ cot $\mathrm{\theta}$_{2}+ cot$\mathrm{\theta}$_{3}= 01. 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 coordinates of the vertices of the square inscribed in the triangle with virtices a(0,0) b(2,1) c(3,0). given that two of its vertices are on the side ac.

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

Find the distance of the point (2,5) from the 3x+y+4=0 measured parallel to a line having slope 3/4.

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.

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

find the equation of the line through the intersection of the lines x+2y-3=0 and 4x -y+7=0 and which is parallel to 5x +4y -20=0.

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.

the 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?

(a) 1

(b) 2

(c) 3

(d) 13

Find the equation of bisector of angle A of triangle whose vertices are A(4,3) , B(0,0) & C(2,3)

Q3. Let coordinates of the points A and B are (5, 0) and (0,7) respectively P and Q are the variable points lying on the x and y -axis respectively so that PQ is always perpendicular to the AB. Then locus of the point of intersection of BP and AQ is

(A)

x^{2}+y^{2}– 5x+ 7y= 0 (B)x^{2}+y^{2}+5x–7y= 0(C)

x^{2}+y^{2}– 5x+ 7y= 0 (D) x^{2}+y^{2}– 5x– 7y= 0How to split a pair of line equation of ax

^{2}+2hxy+by^{2}+2gx+2fy+c=0 in the short method?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.

find the eqn of the line cutting off an intercept -2 from the y-axis and equally inclined to the axes.

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

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

^{ 0}find what the following equation becomes when the origin is shifted to the point(1,1)

x

^{2}+xy-3y^{2}-y+2=0if 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?

Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line

x–2y= 3.Find obtuse angle between lines x-2y+3=0 and 3x +y-1=0

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)

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

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}find the coordinate of the foot of perpendicular form of point (-1,3)to the line(3x-4y-16)=0

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 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 ?

$ax+by+c=0;ax+by+c\text{'}=0;a\text{'}x+b\text{'}y+c=0a\text{'}x+b\text{'}y+c\text{'}=0$ are at right angles. Also find the equation to the diagonals of the parallelogram.

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

If the origin is shifted to the point (2,-1) obtain the new equation of locus,axes remainng parallel.The old equation of locus is:

2x²-3xy-9y²-5x-24y-7=0

1) L+m+n=0

2) L+m-n=0

3) L-m+n=0

4)L^2+m^2+n^2=Lm+mn+nL

~~Put the equation 12y=5x+65 in the form of xcosθ+ysinθ=p and indicate clearly in a rough diagram the position of the straight line and the meaning of the constant θ and p.