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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

Please solve this question with explanation of the solution....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

Find equation of medians of triangle ABC whose vertices are A(2.5) B(-4,9) C (-2,-1)

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?

withparametric form......explanation of the solutionsir, 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

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-

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

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.i) touches the X axis

ii) lies entirely inside the circle x^2 + +y^ = 18

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

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 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 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.

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.

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.

find the locus of a point equidistant from the lines x+y+4=0 and 7x+y+20=0.

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.reduce the equation (root3 x) + y - 8= 0 into normal form. find the values of p and w

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

If (1,2) and (3, 8) are a pair of opposite vertices of a square, find the

equation of the sides and diagonals of the square.

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

^{2}+ y^{2}+ 8x - 6y - 25 = 0 to the form AX^{2}+ BY^{2}= K^{2 }by shifting origin to a suitable point.^{}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.

the point P is the foot of the perpendicular from A(0,t) to the line whose equation is y=tx. Determine

a) the equation of line AP

b) the co-ordinate of P

c) the area of triangle OAP, where O is origin

Find the equation of straight line whose intercepts on the axes are thrice as

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

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.

hence find the distance between (2,-1,3) and (-2,1,3)

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.

Find the equation of the line which lies midway between the lines 2x+3y+7=0 and 2x+3y+5=0the 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?

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

How 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 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 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.

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

Find the equation of a straight line which passes through the point (1,-3) and makes an intercept on y-axis twice as long as on x-axis

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

x

^{2}+xy-3y^{2}-y+2=0find the distance of the point [3,2] from the straight line whose slope is 5 and is passing through the point of intersection of lines x+2y=5and x-3y+5=o

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?

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

x–2y= 3.(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) ${x}^{2}+{y}^{2}-5x-7y=0$

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)

^{2}+1/b^{2}= 1/c^{2}, where c is a constant. the locus of the foot of the perpendicular from the origin on the given line is x^{2}+ y^{2}= c^{2.}If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P.

the points A,Band C are(4,0),(2,2),and(0,6) respectively.AB produced cuts the y-axis at Pand CB produced cuts the x-axis at Q.find the co-ordinates of the pointsP and q.Find the eq. of the straight line joining the mid points of AC nad OB( Where O is the origin )and verify that this line passes through the mid point of PQ.

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 equation of the line passing through the points (a cos alpha, asin alpha) and (acos beta, a sin beta)

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)2. The eqn of base if an equilateral triangle is x+y-2=0 and the opposite vertext has co-ordinates (2,-1) find the area of the triangle.

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 ?

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

~~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.

what acute angle does a line of slope -2/3 make with vertical line.