Straight line joining the points (2, 3) and (-1, 4) passes through the point \((\alpha,\beta)\) if

The slope of the line which makes an angle 45^o with the line 3x- y = -5 are:

Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2\(\sqrt{2}\) is

The coordinates of the four vertices of a quadrilateral are (-2, 4), (-1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (-1, 2) and dividing the quadrilateral in the equal areas is

The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are

The locus of a moving point P(a cos³θ, a sin³θ) is ______________

AB = 12 cm. AB slides with A on x-axis, B on y-axis respectively. Then the radius of the circle which is the locus of ΔAOB, where O is origin is ______________

The equating straight line with y-intercept -2 and inclination with x-axis is 135° is ______________

The length of the perpendicular from origin to line is \(\sqrt{3}x-y+24=0\) is ______________

If(1, 3) (2,1) (9, 4) are collinear then a is ______________

If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x = a cos³ θ, y = a sin³ θ.

Find the value of k and b, if the points P(-3, 1) and Q(2, b) lie on the locus of x² - 5x + ky = 0.

Find the equation of the locus of a point such that the sum of the squares of the distance from the points (3, 5), (1, -1) is equal to 20.

If O is origin and R is a variable point on y² = 4x, then find the equation of the locus of the mid-point of the line segment OR.

The coordinates of a moving point P are \((\frac{a}{2}(cosec\theta+sin\theta),\frac{b}{2}(cosec\theta-sin\theta))\) , where θ is a variable parameter. Show that the equation of the locus P is b²x²- a²y² = a²b²

The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c². Find the equation to its locus.

Find the equation of the lines passing through the point (1, 1) 
(i) with y-intercept (-4)
(ii) with slope 3
(iii) and (-2, 3)
(iv) and the perpendicular from the origin makes an angle 60° with x- axis.

If p (r, c) is mid - point of a line segment between the axes, then show that \(\frac{x}{r}+\frac{y}{c}=2\)

If P is length of perpendicular from origin to the line whose intercepts on the axes are a and b, then show that \(\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}\)

The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F.
(i) Find the linear relationship between C and F.
(ii) Find the value of C for 98.6°F and 
(iii) Find the value of F for 38°C.

Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1.

Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using
(i) concept of slope
(ii) a straight line
(iii) any other method.

Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y - 15 = 0 are paralle llines.

If (-4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x - y + 7 = 0, then find the equation of another diagonal.