Answer
Verified
425.4k+ views
Hint: To solve the above problem we need to know the concept of transformation of the axis, because the question says we have to find the equation of the curve when it has been transferred from the origin to the given point which is the transformation concept.
Complete step-by-step answer:
Let us consider the given as old equation
Old equation is $ \Rightarrow $ $2{x^2} + {y^2} - 3x + 5y - 8 = 0 - - - - - - - > (1)$
From the old equation we say the (x, y) are the old coordinates
Now let (X, Y) be the new coordinates after shifting from origin to new point P (-1, 2) let the point be (h, k).
Now by the concept of transformation of axis we know that
$x = X + h$ $y = Y + K$
Now from using the above concept we can say that,
$x = X - 1$ $y = Y + 2$$ - - - - - - - - - > $(New values)
Now on substituting the new values in equation we get we can write the equation as
$
\Rightarrow 2{(X - 1)^2} + {(Y + 2)^2} - 3(X - 1) + 5(Y + 2) = 0 \\
\Rightarrow 2{X^2} + 1 - 4X + {Y^2} + 4 + 4Y - 3X + 3 + 5Y + 10 = 0 \\
\Rightarrow 2{X^2} + {Y^2} - 7X + 9Y + 18 = 0 \\
$
Thus they mentioned that direction of axis has not changed we have to replace the (X,Y) with (x ,y)
On replacing the values we get equation in form $2{x^2} + {y^2} - 7x + 9y + 18 = 0$
Hence the equation is of ellipse.
Note: In this problem we have considered the coordinates of given equation as old coordinates .And they mentioned that the curve of the equation has been shifted from origin to point p which we have considered as (h, k).Now by using the concept of transformation we have solved the equation. Finally it is mentioned that transformation has been done without changing the direction so as we have replaced the new coordinates with old coordinates.
Complete step-by-step answer:
Let us consider the given as old equation
Old equation is $ \Rightarrow $ $2{x^2} + {y^2} - 3x + 5y - 8 = 0 - - - - - - - > (1)$
From the old equation we say the (x, y) are the old coordinates
Now let (X, Y) be the new coordinates after shifting from origin to new point P (-1, 2) let the point be (h, k).
Now by the concept of transformation of axis we know that
$x = X + h$ $y = Y + K$
Now from using the above concept we can say that,
$x = X - 1$ $y = Y + 2$$ - - - - - - - - - > $(New values)
Now on substituting the new values in equation we get we can write the equation as
$
\Rightarrow 2{(X - 1)^2} + {(Y + 2)^2} - 3(X - 1) + 5(Y + 2) = 0 \\
\Rightarrow 2{X^2} + 1 - 4X + {Y^2} + 4 + 4Y - 3X + 3 + 5Y + 10 = 0 \\
\Rightarrow 2{X^2} + {Y^2} - 7X + 9Y + 18 = 0 \\
$
Thus they mentioned that direction of axis has not changed we have to replace the (X,Y) with (x ,y)
On replacing the values we get equation in form $2{x^2} + {y^2} - 7x + 9y + 18 = 0$
Hence the equation is of ellipse.
Note: In this problem we have considered the coordinates of given equation as old coordinates .And they mentioned that the curve of the equation has been shifted from origin to point p which we have considered as (h, k).Now by using the concept of transformation we have solved the equation. Finally it is mentioned that transformation has been done without changing the direction so as we have replaced the new coordinates with old coordinates.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE